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A rectangle and a square have the same area. The length of the rectangle is seventy feet more than two times its width. The length of a side of the square is thirty feet. What are the dimensions of the rectangle?

A 20 feet wide by 45 feet long
B 30 feet wide by 30 feet long
C 100 feet wide by 900 feet long
D 10 feet wide by 90 feet long
E 60 feet wide by 250 feet long
F 5 feet wide by 180 feet long

2007-05-25 07:35:53 · 5 answers · asked by Nathan C 1 in Science & Mathematics Mathematics

5 answers

Rectangle:
Width = W
Length = 70 + 2W

Square Side = 30

Area of the square is 30^2 = 900.

Area of the rectangle is:
W(70 + 2W)
= 70W + 2W^2

The areas are equal, so

70W + 2W^2 = 900
2W^2 + 70W - 900 = 0
W^2 + 35W - 450 = 0
(W - 10)(W + 45) = 0
W = 10 or -45

We can eliminate the -45 (can't have negative measurement), so
Width = 10
Length = 70 + 2*10 = 90

Answer is D.

2007-05-25 07:43:26 · answer #1 · answered by Mathematica 7 · 0 0

Let the width of the rectangle be x. The length is then 2x+70.
The area of the rectange is thus x*(2x+70)
The area of the square is 30*2=900.
Thus 900=x(2x+70). Simplifying this we get
x^2+35x-450=0, you can factor this to
(x+45) and (x-10)
so x =-45 or 10. The width can't be negative so width =10. and thus length =90 so
Choice D 10 by 90

2007-05-25 14:41:14 · answer #2 · answered by Jon 2 · 0 0

Area of the square will be 30*30=900 sq ft, so rectangle will have same area.
Width of rectangle=x
Length of rectangle=2x+70
The only answer that fits is D. 10 feet wide by 90 feet long.

2007-05-25 14:41:54 · answer #3 · answered by JO 3 · 0 1

The area of the rectangle = area of square = 30^2 = 900 ft^2
w = width of rectangle
so l = 2w+70
So w(2w+70) = 900
2w^2 +70w -900 = 0
w^2+35w -450 = 0
(w+45)(w-10) = 0
w = 10
l= 90
Answer is D

2007-05-25 14:45:57 · answer #4 · answered by ironduke8159 7 · 0 0

D

2007-05-25 14:51:21 · answer #5 · answered by dpr4444 3 · 0 0

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