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?

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  1. rectangle:
    width = x
    length = 3x
    perimeter = 8x
    area = 3x^2

    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

    width = 2
    length = 6
    perimeter = 16
    area = 12

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

    everything checks!

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