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The length of the parallel sides of a trapezium are in the ratio 4:5 and the distance between them is 26 cm . If the area of the trapezium is 468 cm² , find the lengths of its parallel sides.​

Answer 1

Answer:

Given :-

• The length of the parallel sides of a trapezium are in the ratio of 4 : 5 and the distance between them is 26 cm.
• The area of the trapezium is 468 cm².

To Find :-

• What is the length of its parallel sides.

Formula Used :-

$\clubsuit$ Area Of Trapezium Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Area_{(Trapezium)} =\: \dfrac{1}{2} \times (Sum\: of\: Parallel\: Sides) \times Height}}}$

Solution :-

Let,

$\mapsto \bf Length\: of\: first\: side =\: 4x\: cm$

$\mapsto \bf Length\: of\: second\: side =\: 5x\: cm$

Given :

• Distance between them (Height) = 26 cm
• Area of Trapezium = 468 cm²

According to the question by using the formula we get,

$\implies \sf \dfrac{1}{2} \times (4x + 5x) \times 26 =\: 468$

$\implies \sf \dfrac{1}{\cancel{2}} \times 9x \times {\cancel{26}} =\: 468$

$\implies \sf 9x \times 13 =\: 468$

$\implies \sf 9x =\: \dfrac{\cancel{468}}{\cancel{13}}$

$\implies \sf 9x =\: 36$

$\implies \sf x =\: \dfrac{\cancel{36}}{\cancel{9}}$

$\implies \sf\bold{\purple{x =\: 4}}$

Hence, the required length of parallel sides of trapezium are :

❒ Length of first side of trapezium :

$\small\longrightarrow \sf Length\: of\: first\: side_{(Trapezium)} =\: 4x\: cm$

$\small\longrightarrow \sf Length\: of\: first\: side_{(Trapezium)} =\: (4 \times 4)\: cm$

$\small\longrightarrow \sf\bold{\red{Length\: of\: first\: side_{(Trapezium)} =\: 16\: cm}}$

❒ Length of second side of trapezium :

$\small\longrightarrow \sf Length\: of\: second\: side_{(Trapezium)} =\: 5x\: cm$

$\small\longrightarrow \sf Length\: of\: second\: side_{(Trapezium)} =\: (5 \times 4)\: cm$

$\small\longrightarrow \sf\bold{\red{Length\: of\: second\: side_{(Trapezium)} =\: 20\: cm}}$

${\small{\bold{\underline{\therefore\: The\: length\: of\: its\: parallel\: sides\: of\: trapezium\: are\: 16\: cm\: and\: 20\: cm\: respectively\: .}}}}$