Question

two parallel sides of a trapezium and the distance between them are in the ratio 4:3:2 if the area of the trapezium is 1372cm
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Answer 1

Correct Question :-

• Two parallel sides of a trapezium and the distance between them are in the ratio 4:3:2 if the area of the trapezium is 1372cm² then find the parallel sides and height.

Given :-

• Two parallel sides of a trapezium and the distance between them are in the ratio 4:3:2.
• Area of the Trapezium is 1372cm²

To Find :-

• The Measures of Two parallel sides and Height .

Solution :-

Let the First Parallel Side be 4x

Let the Second Parallel Side be 3x

Let the Height of the Parallelogram be 2x

★ According to the Question ★

⇒ Area of Trapezium = ½ × height × sum of parallel sides

⇒ 1372 = ½ × 2x × ( 4x + 3x )

⇒ 1372 = ½ × 2x × 7x

⇒ 1372 = ½ × 14x²

⇒ 1372 = 7x²

⇒ 1372/7 = x²

⇒ 196 = x²

⇒ √196 = x

⇒ 14 = x

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★Measures of Sides and Height★

⇒First Parallel side 4x = 4 × 14 = 56cm

⇒2nd Parallel side 3x = 3 × 14 = 42cm

⇒Height = 2x = 2 × 14 = 28cm

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Verification :-

⇒ Area of Trapezium = ½ × height × sum of parallel sides

⇒ 1372 = ½ × 28 × ( 56 + 42 )

⇒ 1372 = 14 × 98

⇒ 1372 = 1372

Hence, Verified

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