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
A.) 28 m²
B.) 24 m²
C.) 16 m²
D.) 14 m²
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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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
See more geometry word problems here
or
Ask Algebra House