Posted by **Gabby** on Monday, May 10, 2010 at 10:08am.

A rectangle is 3 times as long as it is wide and has the same perimeter as a square whose are is 4 sp.ft. larger than that of the rectangle. What are the dimensions of both the rectangle and the square?

- Math -
**Reiny**, Monday, May 10, 2010 at 2:33pm
rectangle:

width = x

length = 3x

perimeter = 8x

area = 3x^2

square:

side y

perimeter = 4y

area = y^2

perimeters are the same --> 4y = 8x

y = 2x

area of square is 4 more than area of rectangle

y^2 = 3x^2 + 4

4x^2 = 3x^2 + 4

x^2 = 4

x = 2, then y = 4

rectangle:

width = 2

length = 6

perimeter = 16

area = 12

square:

side = 4

perimeter = 16

area = 16 , which is 4 more than that of the rectangle

everything checks!

- Math -
**Joseph**, Monday, May 10, 2010 at 5:27pm
cool

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