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
