Question

A rectangular playground has dimensions and area as shown below.

Complete the work to find the dimensions of the rectangle.

x(4x + 5) = 450

4x2 + 5x = 450

4x2 + 5x – 450 = 0

(4x + 45)(x – 10) = 0

The rectangle has a width, x, of
, and a length of
.

Answer 1

I think it’s 10 because (x-10)=x=10

Answer 2

9514 1404 393

Answer:

• x = 10
• width = 10
• length = 45

Explanation:

The remaining work is to identify the values of x that make the factors zero:

4x +45 = 0

x = -45/4 . . . . negative dimensions are not useful

x -10 = 0

x = 10

The width is x, so the width is 10.

The length is 4x+5, so the length is 4·10+5 = 45.

The rectangle has a width, x, of 10 and a length of 45.