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

The area of an isosceles trapezium is 176 cm^{2} and the height is 2/11^{th} 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

- 28
- √137
- 24
- 2√137

**Answer: (4) 2(137) ^{1/2} cm**

**Explanation:-**s = sum of parallel sides

h = height = 2s/11

V = 176

(2s/11) x s/2 = 176

s^{2}/11 = 176

s^{2}= 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

d^{2} = (8^{2} + 22^{2})^{1/2}

= (64 + 484)^{1/2}

= (548^{1/2}

d = 2(137)^{1/2} cm

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