Question

The height of a trapezoid can be expressed as x - 4, while the bases can be expressed as x + 4 and x + 9. If the area of the trapezoid is 99 cm², find the length of the larger base.

Answer 1

Answer: 19 cm

Explanation:

Substituting into the formula for the area of a trapezoid,

`(1)/(2)(x-4)(x+4+x+9)=99\\\\(1)/(2)(x-4)(2x+13)=99\\\\(x-4)(2x+13)=198\\\\2x^2 +5x-250=0\\\\(2x+25)(x-10)=0\\\\x=-12.5, 10`

However, as x must be positive (since length must be positive), x=10. This means the length of the longer base is 19 cm.