Question

Find the dimension of a rectangle whose width is 10 miles less than its length and whose area is 75 square miles

Answer 1

Answer:

The length is 15 miles and the width is 5 miles.

Step-by-step explanation:

The rectangle has two dimensions, width w and length l.

The area is given by the following formula:

$S = wl$.

In this problem, we have that:

The width is 10 miles less than its length. This means that

$w = l - 10$

The area is 75 square miles. So

$wl = 75$

$(l - 10)l = 75$

$l^{2} - 10l - 75 = 0$.

$l = 15$ and $l = -5$.

We cannot have negative dimensions. This means that the length is 15 miles and the width is 5 miles.

Answer 2

W = L - 10
75 = L × ( L - 10 )
75 = L^2 - 10L
L^2 - 10L - 75 = 0
( L - 15 ) ( L + 5 ) = 0
L = 15

w = 15 - 10
w = 5

2 dimension