Question

The length of one base of a trapezoid is 19 less than five times the length of the other base. If the trapezoid has a height of 18 feet and an area of 477 ft squared, find the length of the longer base

Answer 1

The length of longer base is 41 feet

Solution:

The area of trapezoid is given as:

$A = \frac{a+b}{2} \times h$

Where , "a" and "b" is the length of base and "h" is the height

The length of one base of a trapezoid is 19 less than five times the length of the other base

a = 19 less than fives times b

a = 5b - 19

Height of 18 feet and an area of 477 ft squared

h = 18 feet

area = 477 square feet

Substitute the values in above formula

$477=\frac{5 b-19+b}{2} \times 18\\\\477=(6b-19) \times 9\\\\477 = 54b-171\\\\54b = 648\\\\b=12$

Therefore,

a = 5b - 19 = 5(12) - 19 = 41

Thus length of longer base is 41 feet