Question

The area of an isosceles trapezium is $168$ sq.metres. If the length of the parallel sides are $36mand20m$ respectively. Find the length of the non-parallel sides.

• A. $10m,10m$
• B. $20m,20m$
• C. $20m,10m$
• D. None of these

Answer 1

The correct option is A $10m,10m$

Let the length of non parallel side$=c$
Area of isosceles trapezium $=\frac{1}{4}\sqrt{{(a+b)}^2(a-b+2c)(b-a+2c)}$
$168=\frac{1}{4}\sqrt{{(20+36)}^2(36-20+2c)(20-36+2c)}$
Squaring both the side
$28224=\frac{1}{16}\left(3136\right)(4c^2-256)$
$28224=196(4c^2-256)$
$28224=784c^2-50176$
$784c^2=28224+50176$
$784c^2=78400$
$c^2=100$
$c=10m$
Since in isosceles trapezium length of non parallel side is equal thus the length will be $10m,10m$