SOLUTION: The perimeter of an isosceles trapezoid is 28 in and the ratio of lengths of its bases is 5:3. Find the lengths of the sides of the trapezoid if its diagonal bisects the angle at t

Algebra ->  Points-lines-and-rays -> SOLUTION: The perimeter of an isosceles trapezoid is 28 in and the ratio of lengths of its bases is 5:3. Find the lengths of the sides of the trapezoid if its diagonal bisects the angle at t      Log On


   

Question 1114226: The perimeter of an isosceles trapezoid is 28 in and the ratio of lengths of its bases is 5:3. Find the lengths of the sides of the trapezoid if its diagonal bisects the angle at the longer base.
Answer by ikleyn(52776) About Me  (Show Source):
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Make a sketch and find an isosceles triangle formed by the diagonal, shorter base and the lateral side of the trapezoid.


Thus you have the lateral sides of the trapezoid congruent to the shorter base.


Your trapezoid then has the sides of 5:3:3:3 units.


In total, there are 5 + 3 + 3 + 3 = 14 units.


Hence, each unit is of   28%2F14 = 2 inches long and the sides are of  6 in,  6 in,  6 in  and  10 in.

Solved.