Question

The area of a trapezium is 1586 cm sq and the distance between its parralel sodes os 26 cm. If one of the parallel sodes is 84 cm fond the other

Answer 1

Question :-

• The Area of a trapezium is 1586 cm² and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, Find the other.

Given :-

• Area of the trapezium = 1586 cm²

• Distance between its parallel sides (height) = h = 26 cm

• Length of one parallel sides of the trapezium = 84 cm

To Find :-

• Length of the other parallel sides of the trapezium.

Solution :-

Let the other parallel side be x.

We know that,

$\leadsto\:\:\underline{\boxed{\pink{\sf{Area\:of\:trapezium = \dfrac{1}{2} \times h \times (Sum\:of\:parallel \:sides)}}}}$

So,

$:\implies\:\:\:\sf{1586 = \dfrac{1}{2} \times 26 \times (84 +x) }$

$:\implies\:\:\:\sf{1586 = \dfrac{26}{2} \times (84 +x) }$

$:\implies\:\:\:\sf{1586 = 13 \times (84 +x) }$

$:\implies\:\:\:\sf{84 +x=\dfrac{1586}{13} }$

$:\implies\:\:\:\sf{84 +x=122}$

$:\implies\:\:\:\sf{x=122-84}$

$:\implies\:\:\:\sf{x=38}$

∴ Other parallel side of the trapezium = 38 cm.