Question

A square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is 84 square inches. Write an equation you can use to find the width (in inches).

Answer 1

So side of square=w/2

• Area cut=w²/2²=w²/4

So

area of rectangle=14w

Hence

• 14w-w²/4=84
• 56w-w²=336
• w²-56w+336=0

Answer 2

• See below

Explanation:

The side of the square is w/2, then its area is:

• A = (w/2)² = w²/4

The shaded area is the difference of areas of the rectangle and the square:

• 14w - w²/4 = 84

This can be simplified:

• 56w - w² = 336
• w² - 56w + 336 = 0