If the area of the trapezoid is 196 cm squared, a = 5x - 2cm, b = x+ 3 cm, and h = 8cm, calculate the length of the longer base.

Question

a is the bottom base, b is the top base, and h is the height.

Answer 1

Area = (1/2)(b₁+b₂)h

Area = (1/2)(a+b)h

196 = (1/2)[(5x-2)+(x+3)](8)

196 = (1/2)(6x+1)(8)

196 = 4(6x+1)

196 = 24x+4

192 = 24x

8 = x

Calculating the length of each base:

a = 5x-2 cm = 5(8)-2 cm = 40-2 cm = 38cm

b = x+3 cm = 8+3 cm = 11cm

Therefore, a = 38cm is the length of the longer base.

Hope this helped!