# Find the Length of a Diagonal (in cm) :

The area of an isosceles trapezium is 176 cm2 and the height is 2/11th of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4:7, then the length of a diagonal (in cm) is

1. 28
2. √137
3. 24
4. 2√137
Anurag Mishra Professor Asked on 26th October 2015 in

Explanation:-
s = sum of parallel sides
h = height = 2s/11

V = 176
(2s/11) x s/2 = 176
s2/11 = 176
s2= 11 x 176
= 1936
s = 44 cm

Ratio of parallel sides =  4:7
Shorter parallel side = 4 x 44/11
4 x 4 = 16
Longer parallel side = 7 x 44/11
7 x 4 = 28

Now
So, 28−16 = 12 and 12/2 = 6
So longer parallel base sticks out 6 cm more than shorter base at each end.
Draw a figure

Vertical distance from one end of diagonal to the other
h = 2 x 44/11
2 x 4 = 8
Horizontal distance from end of diagonal to the other = 16+6
= 22 cm

d2 = (82 + 222)1/2
= (64 + 484)1/2
= (5481/2
d = 2(137)1/2 cm

Hence, the answer is (4)  2(137)1/2 cm.

Monis Rasool Professor Answered on 28th October 2015.