Perimeter and Area of Rectangle Word Problem

The base of a rectangle is seven times the height.  If the perimeter is 32 meters, what is the area?
A.)  28 m²
B.)  24 m²
C.)  16 m²
D.)  14 m²

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h = height of rectangle
7h = base of rectangle   {base is seven times the height}

Perimeter of a rectangle = 2(height) + 2(base)

2h + 2(7h) = 32   {perimeter is 2(height) + 2(base)}
2h + 14h = 32   {multiplied 2 by 7h}
16h = 32   {combined like terms}
h = 2   {divided each side by 16}
7h = 14   {substituted 2, in for h, into 7h to find base}

height is 2 m  and the base is 14 m

Area of rectangle = base x height
= 2(14)   {base x height}
= 28   {multiplied}

A.)  28 m²

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