Figure ABCD is a square. Side AB measures 10x – 7. Side BC measures 2x + 52. Find the value of x.

It is a square so those sides are equal.

10 x - 7 = 2 x + 52

8 x = 59

x = 59/8

To find the value of x, we can equate the length of side AB to the length of side BC.

Given:
AB = 10x - 7
BC = 2x + 52

Since ABCD is a square, opposite sides have the same length. Therefore, AB = BC.

Setting up the equation:
10x - 7 = 2x + 52

Now, to solve for x, we can perform the following steps:

1. Move all the terms containing x to one side of the equation:
10x - 7 - 2x = 2x + 52 - 2x
8x - 7 = 52

2. Move the constant term (-7) to the other side of the equation:
8x - 7 + 7 = 52 + 7
8x = 59

3. Solve for x by dividing both sides of the equation by 8:
8x/8 = 59/8
x = 59/8

Hence, the value of x is 59/8.