Question

The area rug in your living room is 5 feet longer than it is wide. If the rug is

Answer 1

Answer:

length = 17 ft and width = 12 ft

Step-by-step explanation:

The rug is rectangular .

Let

width = a

length = a + 5

Area of the rug = a × (a + 5) = a² + 5a

The rug is always placed 2 ft from the wall. The illustration describes a rectangle place into another. The space between the rug and the wall is 100 ft².  

The living room

length = a + 5 + 2 + 2= a + 9

width  = a + 2 + 2 = a + 4

area = (a + 9)(a + 4) = a² + 4a + 9a + 36 = a² + 13a + 36

a² + 13a + 36 - (a² + 5a) = 100

a² + 13a + 36 - a² - 5a = 100

8a + 36 = 100

8a = 100 - 36

8a = 64

a = 64/8

a = 8

Dimension of the living room

length = a + 9

length = 8 + 9 = 17 ft

width  = a + 4

width = 8 + 4 = 12 ft

length = 17 ft and width = 12 ft