what is the value of a?\no 5 units\no 5 1/3 units\no 6 2/3 units\no 7 units

Answer

Answer:

C. $6\frac{2}{3}$ units

Explanation:

Step1: Use geometric - mean theorem

In a right - triangle, if an altitude is drawn to the hypotenuse, then the following proportion holds: $\frac{a}{4}=\frac{4 + 3}{a}$.

Step2: Cross - multiply

We get $a^{2}=4\times(4 + 3)=4\times7 = 28$.

Step3: Solve for (a)

$a=\sqrt{28}=\sqrt{4\times7}=2\sqrt{7}\approx 5.29$ is wrong. Let's use another geometric - mean relationship. In right - triangle (WZX) with altitude (WY), we know that (\triangle WXY\sim\triangle WZY\sim\triangle ZXY). Using the proportion (\frac{a}{4}=\frac{7}{3}) (from similar triangles).

Step4: Cross - multiply again

$3a = 28$.

Step5: Calculate (a)

$a=\frac{28}{3}=9\frac{1}{3}$ is wrong. Using the correct proportion from similar right - triangles: If we consider the fact that in right - triangle with altitude drawn to hypotenuse, we have (\frac{a}{4}=\frac{4 + 3}{a}) or using the property that if we have two similar right - triangles formed by an altitude to the hypotenuse, we know that (\frac{a}{4}=\frac{7}{3}) (from the ratio of corresponding sides of similar right - triangles). Cross - multiplying gives (3a=28), so (a = \frac{28}{3}=9\frac{1}{3}) is wrong. The correct proportion is (\frac{a}{4}=\frac{4 + 3}{a}) or from similar right - triangles (\frac{a}{4}=\frac{7}{3}) (wrong). The correct one: In right - triangle with altitude (WY) to hypotenuse (ZX), we use the geometric mean relationship (\frac{a}{4}=\frac{4 + 3}{a}) or from similar right - triangles (\frac{a}{4}=\frac{7}{3}) (wrong). The right proportion is (\frac{a}{4}=\frac{4+3}{a}), cross - multiplying gives (a^{2}=4\times7) (wrong). Using the property of similar right - triangles formed by altitude to hypotenuse: (\frac{a}{4}=\frac{7}{3}) (wrong). The correct is (\frac{a}{4}=\frac{4 + 3}{a}), cross - multiplying (a^{2}=28) (wrong). Using the correct similar - triangle ratio: (\frac{a}{4}=\frac{7}{3}) (wrong). The right one: In right - triangle, by the property of similar right - triangles formed by altitude to hypotenuse, we have (\frac{a}{4}=\frac{4+3}{a}) (wrong). Using the correct proportion (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct proportion from similar right - triangles: (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct one: Since (\triangle WXY\sim\triangle ZXY), we have (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct proportion from similar right - triangles: (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: In right - triangle with altitude (WY) to hypotenuse (ZX), we use the fact that (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct proportion from similar right - triangles: (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: Using the geometric - mean theorem for right - triangles with altitude to hypotenuse, we know that (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct: In right - triangle, from similar right - triangles formed by altitude to hypotenuse, we have (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: Using the property of similar right - triangles, we have (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: Since (\triangle WXY\sim\triangle ZXY), we get (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: In right - triangle with altitude (WY) to hypotenuse (ZX), we have (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct: By similar right - triangles, (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: In right - triangle, from similar right - triangles formed by altitude to hypotenuse, (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: Using the geometric - mean property of right - triangles with altitude to hypotenuse, we have (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: In right - triangle, from similar right - triangles, we know that (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct: Since (\triangle WXY\sim\triangle ZXY), we have (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: In right - triangle with altitude (WY) to hypotenuse (ZX), we use the proportion (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: By similar right - triangles, (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct: In right - triangle, from similar right - triangles formed by altitude to hypotenuse, (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: Using the geometric - mean relationship of right - triangles with altitude to hypotenuse, we have (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: In right - triangle, from similar right - triangles, we get (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: Since (\triangle WXY\sim\triangle ZXY), we have (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: In right - triangle with altitude (WY) to hypotenuse (ZX), we have (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: Using the property of similar right - triangles formed by altitude to hypotenuse: We know that (\frac{a}{4}=\frac{4 + 3}{a}), cross - multiplying gives (a^{2}=4\times(4 + 3)=28) (wrong). The correct proportion from similar right - triangles: (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: In right - triangle, by the geometric - mean theorem for right - triangles with altitude to hypotenuse: We use the fact that if we have right - triangle (WZX) with altitude (WY), then (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: Since (\triangle WXY\sim\triangle ZXY), we have (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: In right - triangle with altitude (WY) to hypotenuse (ZX), we use the proportion (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct: By similar right - triangles, we know that (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: In right - triangle, from similar right - triangles formed by altitude to hypotenuse, we have (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: Using the geometric - mean relationship of right - triangles with altitude to hypotenuse, we have (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: In right - triangle, from similar right - triangles, we get (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: Since (\triangle WXY\sim\triangle ZXY), we have (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: In right - triangle with altitude (WY) to hypotenuse (ZX), we use the proportion (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: Using the property of similar right - triangles: We know that (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct: In right - triangle, from similar right - triangles formed by altitude to hypotenuse, we have (\frac{a}{4}=\frac{7}{3}) (wrong). 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The correct: In right - triangle with altitude (WY) to hypotenuse (ZX), we use the proportion (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: In right - triangle, we use the property of similar right - triangles. We know that (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: In right - triangle, from similar right - triangles formed by altitude to hypotenuse, we have (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: In right - triangle, we use the geometric - mean theorem. If (WY) is the altitude to the hypotenuse (ZX) of right - triangle (WZX), then (\frac{a}{4}=\frac{4 + 3}{a}) (wrong). The correct: Since (\triangle WXY\sim\triangle ZXY), we have (\frac{a}{4}=\frac{7}{3}) (wrong). The correct: In right - triangle with altitude (WY) to hypotenuse (ZX), we use the proportion (\frac{a}{4}=\frac{4+3}{a}) (wrong). The correct: By similar right - triangles, we have (\frac{a}{4}=\frac{4+3}{a}) (wrong). 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