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.

We are given the
perimeter of isosceles trapezoid = 28 in
ratio of length of bases = 5:3

We are to find the lengths of sides of the trapezoid and the diagonal that bisects the angle at the base with a longer length

The formula for the perimeter of an isosceles trapezoid is
P = (1/2) (b1 + b2) h

We are given the ratio
b2/ b1 = 5 /3
b2 = 5/3 b1
Substituting
28 = (1/2) (5/3 b1) h
The height of the trapezoid is expressed in terms of b1
For the diagonal
d² = h² + [(b2 - b1) + (b2 - b1)/2]²
Express h and b2 in terms of b1 and diagonal can be expressed in terms of b1