Question

One base of a trapezoid is 8 cm longer than the other. The height of the trapezoid is 2 cm longer than the shortest base. If the area is 48 cm2, what are the height and bases?

A. The height is 6 cm, and the bases are 4 cm and 12 cm.
B. The height is 12 cm, and the bases are 10 cm and 18 cm.
C. The height is 4 cm, and the bases are 2 cm and 10 cm.
D. The height is 10 cm, and the bases are 8 cm and 16 cm.

Answer 1

B

Explanation:

Let's call the shortest side a. The longest base, b, is 8cm longer than a. The height, h, is 2cm longer than a.

b = a + 8

h = a + 2

A = (a + b)h/2

48 = (a + (a+8))(a+2)/2

= (2a+8)(a+2)/2

= (2a^2+12a+16)/2

48 = a^2+6a+8

a^2+6a-40=0

Now, we factor this:

(a + 4)(a - 10)=0

a = -4, 10

a (length) cannot be a negative no. so the only possible answer is a = 10.

b = 10 + 8 = 18

h = 10 + 2 = 12

The answer is B

Hope this helps!