what is the perimeter of trapezoid jklm?\n√2 + √5 units\n2 + √2 + √5 units\n9 + 2√2 units\n9 + √2 + √5…
what is the perimeter of trapezoid jklm?\n√2 + √5 units\n2 + √2 + √5 units\n9 + 2√2 units\n9 + √2 + √5 units\nj(-7,4) k(-4,4)\nm(-8,3) l(-2,3)
Answer
Explanation:
Step1: Calculate length of JK
Since J(-7,4) and K(-4,4) have same y - coordinate, use distance formula for horizontal line. $JK=\vert-4 - (-7)\vert=3$.
Step2: Calculate length of KL
K(-4,4) and L(-2,3). Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. $KL=\sqrt{(-2+4)^2+(3 - 4)^2}=\sqrt{4 + 1}=\sqrt{5}$.
Step3: Calculate length of LM
L(-2,3) and M(-8,3) have same y - coordinate. $LM=\vert-8+2\vert = 6$.
Step4: Calculate length of MJ
M(-8,3) and J(-7,4). Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. $MJ=\sqrt{(-7 + 8)^2+(4 - 3)^2}=\sqrt{1+1}=\sqrt{2}$.
Step5: Calculate perimeter
Perimeter $P=JK + KL+LM+MJ=3+\sqrt{5}+6+\sqrt{2}=9+\sqrt{2}+\sqrt{5}$.
Answer:
$9+\sqrt{2}+\sqrt{5}$ units