Question

The two parallel sides of a trapezium are in the ratio 5:7 and the distance between them is 11cm. if the area of trapezium is 396cm square, find the lengths of the parallel sides.​

Answer 1

Answer :-

• The lengths of the parallel sides of the trapezium are 30 cm and 42 cm.

To find :-

• The lengths of the parallel sides of the trapezium.

Step-by-step explanation :-

• Here, it is given that the two parallel sides of a trapezium are in the ratio 5 : 7 and the distance between them is 11 cm. We have to find the lengths of the parallel sides if the area of the trapezium is 396 cm².

We know that :-

$\underline{\boxed{\sf{Area_{(trapezium)} = \dfrac{1}{2} \times (a + b) \times d}}}$

Where,

• a and b = Parallel sides.
• d = Distance.

Let :-

• The parallel sides of trapezium as 5x and 7x.

Therefore :-

$\sf{\longrightarrow \: \dfrac{1}{2} \times (5x + 7x) \times 11 = 396}$

$\sf{\longrightarrow \: \dfrac{1}{2} \times 12x \times 11 = 396}$

$\sf{\longrightarrow \: 12x \times 11 = 396 \times 2}$

$\sf{\longrightarrow \: 12x \times 11 = 792}$

$\sf{\longrightarrow \: 12x = \dfrac{792}{11}}$

$\sf{\longrightarrow \: 12x = 72}$

$\sf{\longrightarrow \: x = \dfrac{72}{12}}$

$\sf{\longrightarrow \: x = 6}$

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Hence, the lengths of the parallel sides of the trapezium are :-

$\bf5x = 5 \times 6 = 30 \: cm.$

$\bf 7x = 7 \times 6 = 42 \: cm.$

Answer 2

Length are 30 and 42 cm

Hope it helps you