Tonya has a rectangular rug .The rug is 4 feet longer than it is wide.

Question

(Part A) Create an expression that can be used to determine the length and the width of the rug. Write your answers in terms of x. *

(Part B) Tonya adds a 1.5-foot border all the way around the rug. Write an expression to represent the length and width of the of the rug.

Answer 1

Part A: Use the area formula for a rectangle, A = w × l.

Set the longer dimension of the rectangle to the variable w, the area of the rectangle to 21, and the shorter side of the rectangle to w – 4.

A=w(w-4)=21

w^2-4w-21=0

I can factor the left side by noting that –7 × 3 = –21 and –7 + 3 = –4.

(w-7)(w+3)=0

property of 0 that if a × b = 0, then either a = 0, b = 0, or both a and b = 0.

If (w–7) = 0, then w is 7, and if (w+3) = 0, then w is –3. The width can’t be less than zero, so the –3 isn’t useful in the context of the problem. That leaves a width of 7 feet. The other dimension is 4 feet less than that, so 3 feet.

Part B: Use the area formula for a rectangle, A = w × l.

The new dimension of the rug, with a 1.5-foot border added on each of the four sides is (7 + 1.5 + 1.5) feet by (3 + 1.5 + 1.5) feet.

A= (10)(6)

A=60