a square picture with a side length of 4 inches needs to be enlarged. the final area needs to be 81 square…
a square picture with a side length of 4 inches needs to be enlarged. the final area needs to be 81 square inches. which equation can be used to solve for x, the increase in side length of the square in inches? x² + 4x - 81 = 0 x² + 4x - 65 = 0 x² + 8x - 65 = 0 x² + 8x - 81 = 0
Answer
Explanation:
Step1: Find the new side - length expression
The original side - length of the square is 4 inches. If the side - length is increased by (x) inches, the new side - length is ((x + 4)) inches.
Step2: Use the area formula for a square
The area (A) of a square is (A=s^{2}), where (s) is the side - length. We know the final area (A = 81) square inches. So, ((x + 4)^{2}=81).
Step3: Expand the left - hand side
Expand ((x + 4)^{2}) using the formula ((a + b)^{2}=a^{2}+2ab + b^{2}), where (a=x) and (b = 4). We get (x^{2}+8x + 16=81).
Step4: Rearrange the equation
Subtract 81 from both sides of the equation: (x^{2}+8x+16 - 81=0), which simplifies to (x^{2}+8x - 65=0).
Answer:
(x^{2}+8x - 65 = 0) (corresponding to the third option)