Question

12. The area of a trapezium is 279 sq. om and
the distance between its two parallel sides is
18 cm. If one of its parallel sides is longe
than the other side by 5 cm, find the lengths
of its parallel sides.​

Answer 1

Given :-

• The area of a trapezium is 279 sq. cm .

• The distance between its two parallel sides is 18 cm.

• One of its parallel sides is longer than the other side by 5 cm.

To Find :-

• The lengths of its parallel sides.

Solution :-

Consider one side be x

& another (x + 5)

We know,

The area of a trapezium is =

$\dfrac{1}{2} \times sum \: of \: parallel \: side \: \times hieght$

The area of a trapezium is 279 sq. cm

➝ The area of a trapezium is = $\dfrac{1}{2} \times l1 \times l2 \: \times hieght$

➝ 279 = ½ × ( x + x + 5 ) × 18

➝ 279 = ½ × (2x + 5) × 18

➝ 279 = 9 (2x + 5)

➝ 279 = 18 x + 45

➝ 279 - 45 = 18 x

➝ 234 = 18x

➝ x = $\cancel{\dfrac{234}{18}}$

➝ x = 13 cm

Hence, first side be x = 13 cm

& another (x + 5) = 13 + 5 = 18 cm

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Answer 2

To Find:-

• Find the lengths of the parallel sides.

Given:-

• The area of trapezium is 279.
• The distance between the parallel sides of 18 cm.
• If one of its parallel sides is longer than other sides by 5 cm.

Solution:-

️ ➭ Sum of parallel sides = (Area × 2)/Height

️ ➭ Sum = (279 × 2)/18

️ ➭ Sum = 558/18

️ ➭ Sum = 31

Let longer side of parallelogram be x + 5

The shorter side of parallelogram be x

️ ➭ x + x + 5 = 31

️ ➭ 2x + 5 = 31

️ ➭ 2x = 31 - 5

️ ➭ 2x = 26

️ ➭ x = 26/2

$\boxed{\bf{\color{black}{ \: x \: = \: 13 \: }}}$

The shorter side is 13.

The longer side is 18.