## 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 –

Question

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

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3 years 2021-07-30T23:29:16+00:00 2 Answers 49 views 0

x2 + 8x – 65 = 0

Step-by-step explanation:

Complete question

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

Given the initial side length = 4in

Initial area = L²

L is side length of the square

Initial area = 4²

Initial area = 16 square inches

Area of the enlarged square = 81 square inches

To get the constant term of the expression, we will find the difference in the areas

Difference = 85 – 16

Difference = 65 square units

The coefficient of x will be the 2 *initial area of the square

Given the standard form of an expression as

ax^2 + bx + c

a = 1, b = 2*4 = 8, c = -65

Substitute

x^2 + 8x – 65

This gives the required expression