SOLUTION: A trapezoid has an area of 360m^2 and an altitude of 20m. Its two bases have ratio 4:5. What are the lengths of the shorter bases ?

Algebra ->  Length-and-distance -> SOLUTION: A trapezoid has an area of 360m^2 and an altitude of 20m. Its two bases have ratio 4:5. What are the lengths of the shorter bases ?      Log On


   

Question 939411: A trapezoid has an area of 360m^2 and an altitude of 20m. Its two bases have ratio 4:5. What are the lengths of the shorter bases ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the area of a trapezoid is:
A=%28%28a%2Bb%29%2F2%29%2Ah+
given:
A=360m%5E2
h=20m
a%3Ab=4%3A5=> 5a=4b=> a=4b%2F5

360m%5E2=%28%284b%2F5%2Bb%29%2F2%29%2A20m+....solve for b



360m=%289b%2F5%29%2A10+

360m%2A5=90b+

1800m%2F90=b+

highlight%28b=20m+%29
now find a

a=4b%2F5
a=%284%2A20m%29%2F5
a=%284%2Across%2820%294m%29%2Fcross%285%29
a=4%2A4m%29
highlight%28a=16m%29 =>the lengths of the shorter bases