Question

An envelope has a perimeter of 30 inches. Its area is 50 square inches. What are the dimensions of the

envelope?
inches by
inches

Answer 1

The dimensions of the envelope are 5 by 10 inches.

Explanation:

Perimeter formula for a rectangle: P = 2W + 2L

Area formula ' " " A = W*L

Here, P = 2W + 2L, so 30 in = 2W + 2L, or 15 in = W + L

Also, A = W*L, so 50 in^2 = W*L, or (if we solve this for W) W = (50 in)/L

But 15 = W + L, or 15 - L = W. Substitute this result for W in the equation W = (50 in)/L:

We get (50 in)/L = 15 - L

Multiplying both sides by L eliminates the fraction:

50 in = 15L - L^2, or

L^2 - 15L + 50 = 0

This factors into (L - 10)(L - 5) = 0, so L is either 10 or 5. Because 15 - L = W, W is either 10 or 5.

The dimensions of the envelope are 5 by 10 inches.

Answer 2

10in by 5in

Explanation:

PERIMETER: p=2(a+b) p=30

AREA: A=a×b A=50

2(a+b)=30

a×b=50