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24 May, 18:18

The rectangle is 2 cm wider and 5 cm longer than a square. The area of the rectangle is 38 cm greater than the square. What are the dimensions of the rectangle?

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  1. 24 May, 18:23
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    the rectangle has dimensions of 6cm x 9 cm

    Step-by-step explanation:

    denoting as 'a' the shorter side of the rectangle, 'b' as the longer side of the rectangle and 'L' as the side length of the square, then

    a=L+2

    b=L+5

    the area Aof the rectangle is

    A=a*b

    since the area is of the square is L², then

    A=38+L²

    replacing the values

    A = (L+2) * (L+5) = L² + 5*L+2*L+10 = L² + 7*L + 10

    38+L² = L² + 7*L + 10

    38 = 7*L + 10

    7*L = 28

    L = 28/7 = 4 cm

    then from the first equations

    a=L+2 cm = 4 cm + 2 cm = 6 cm

    b = L + 5 cm = 4 cm + 5 cm = 9 cm

    therefore the rectangle has dimensions of 6cm x 9 cm
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