A trapezoid has an area of 144 square meters and an altitude of 4 meters. Its two bases have a ratio of 4:5. What is the perimeter of the trapezoid?

Question

10083 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-14T16:39:10

#x + g(x) + 72#

#b/B = 4/5#

#A = (B + b)/2 cdot h#

#144 = (B + 4/5 B)/2 cdot 4#

#72 = B + 4/5 B = 9/5 B Rightarrow B = 5/9 cdot 72 = 40#

#b = 4/5 cdot 40 = 32#

#B - b = 8#

There are infinitely many #x#'s , #y#'s such that the area of triangle is #1/2 cdot 8 cdot 4 = 16#

enter image source here

Heron's formula: #2p = x + y + 8#

#16 = sqrt{p(p-x)(p-y)(p-8)} = f(x, y)#

We want trapezoid's perimeter = #x + y + 40 + 32#