Question

The length of a rectangular room is 9 feet longer than twice the width. If the​ room's perimeter is 150 ​feet, what are the​ room's dimensions?

Answer 1

Length = 53 feet

Width = 22 feet

Explanation:

Perimeter = 2(length + width)

Then:

a = 2w + 9 Ec. 1

150 = 2(a + w) Ec. 2

a = length

w = width

From Eq. 1:

a - 9 = 2w Eq. 3

From Eq. 2:

150 = 2*a + 2*w

150 = 2a + 2w

150 - 2a = 2w Eq. 4

Equalizing Eq. 3 and Eq. 4

a - 9 = 150 - 2a

a + 2a = 150 + 9

3a = 159

a = 159/3

a = 53

From Eq. 1:

a = 2w + 9

53 = 2w + 9

53 - 9 = 2w

44 = 2w

44/2 = w

w = 22

Check:

From Eq. 2

150 = 2(a+w)

150 = 2(53+22)

150 = 2*75