# Math

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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 -

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!

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