Question

The area of a trapezium is 176 cm2
, The distance between
its parallel sides is 8 cm and one of the parallel sides is of length
10 cm. The length of the other side is

Answer 1

Answer:

The Lenght of other side = 34 cm

Answer 2

Answer :-

• Length of other side = 34 cm.

Explanation :-

Given :

• The area of trapezium is 176 sq.cm.

• The distance between its parallel sides is 8 cm and one of the parallel sides is of 10 cm.

To Find :

• Length of other side.

Solution :

Formula Used :-

$\boxed{\sf{Area \: of \: trapezium = \dfrac{1}{2} \bigg(p_{1}+ p_{2}\bigg) h}}$

So, Put the Values.

$\implies\sf{\dfrac{1}{2} \bigg(10+ p_{2}\bigg) 8= 176 \: {cm}^{2} }$

$\implies\sf{4\bigg(10+ p_{2}\bigg) = 176 \: {cm}^{2} }$

$\implies\sf{40+ 4p_{2} = 176 \: {cm}^{2} }$

$\implies\sf{4p_{2} = 176 - 40 }$

$\implies\sf{4p_{2} = 136 }$

$\implies\sf{p_{2} = \dfrac{136}{4} }$

$\implies\underline{\boxed{\sf\red{p_{2} = 34 \: cm } }}$

Therefore, Length of other side = 34 cm.

Verification :-

$\sf{Area \: of \: trapezium = \dfrac{1}{2} \bigg(p_{1}+ p_{2}\bigg) h}$

$\implies\sf{176 = \dfrac{1}{2} \bigg(10+34\bigg) 8}$

$\implies\sf{176 \: = \dfrac{1}{2} \times 44 \times 8}$

$\implies\sf{176 \: = 22 \times 8}$

$\implies\sf{176 \: = 176}$

LHS = RHS.

Hence, Verified.