Question

Use the algebraic expressions for the length and width of Marlene's living room found in the

23.
diagram and the value of x found in Question 21C.
A. Find the actual length and width of her living room.
B
Find the actual area of Marlene's living room. Use actual dimensions.

Answer 1

The area of Marlien's living room is 420 square ft

Explanation:

Before calculating the real dimensions of Marlien's living room, we must find the value of x.

Given the total shape of the house is a rectangle, then both widths must be equal and both lengths must be equal.

The widths are already written width identical expressions x-2+x, but the lengths are given as different functions of x. Equating both expressions, we have:

`2x-10+x-2+(1)/(2)x-4+x-2=2x+2+(1)/(2)x-4+x-2`

Simplifying:

-10 + x - 2 = 2

x = 10 + 2 + 2

x = 14

Since x=14 feet, the dimensions of Marlien's living room are

width=x=14 feet

length=2x+2=30 feet

Thus the area is:

A = 14*30 = 420 square ft

The area of Marlien's living room is 420 square ft