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A rectangular banquet room has an area of 182 square meters and a perimeter of 54 meters. Let l and w represent the dimensions of the room in meters. Which statements describe the dimensions of the banquet room? Select all that apply.

A rectangular banquet room has an area of 182 square meters and a perimeter of 54 meters-example-1
User Sapph
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1 Answer

16 votes
16 votes

Answer:

Choose all but C

Explanation:

Givens

Area = 182 m^2

Perimeter = 54 m

Solution.

B: solves for the length, not the width. Area = L*w. Area / w = L. But to get to the length, you need to solve for the width. So this statement can be used. B is true.

C is not true. The length and width differ by 1 which means one of them is even and the other is odd. See below under A.

D is also true. 2L = 54 - 2w Divide both sides by 2

2L/2 = 54/2 - 2w/2

L = 27 - w

E is true.

L * w = 182 Divide both sides by w

L = 182/w

The only one we don't know about is A. We have to solve the problem to get the answer to A.

P= 2L + 2w = 54

2L + 2w = 54

L + w = 27

L = 27 - w

L*w = 182

(27 - w ) * w = 182 Remove the brackets

27w - w^2 = 182 Subtract 27w - w^2 from both sides.

0 = w^2 - 27w + 182 Notice the sign change. Subtraction does that.

This factors into

(w - 13)(w - 14)

A turns out to be true, because w can be 13 or 14. When W = 13, L = 14.

When w = 14, L = 13

User Bwc
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