Question

The parallel sides of a trapezium are in the ratio 3 : 4. If the distance between the parallel sides is 9 dm and its area is 126dm
2
, find the lengths of smallest its parallel sides.

Answer 1

$\sf{\huge{\underline{\orange{Given :-}}}}$

• The parallel sides of a trapezium are in the ratio 3 : 4.

• The distance between the parallel sides is 9 dm .

• The area of given trapezium is 126 dm².

$\sf{\huge{\underline{\blue{To\:Find :-}}}}$.

• The lengths of smallest parallel side.

$\sf{\huge{\underline{\green{Solution :-}}}}$

Let the legth be in form of x,

The parallel sides of a trapezium are in the ratio 3 : 4.

Such that, 3x & 4x

The height is 9 dm

We know that the area of triangle,

➝ ½ × sum of || sides × height

➝ ½ × (3x + 4x) × 9 ------(1)

The area of given trapezium is 126 dm².------(2)

From Equation. 1 & 2

½ × (3x + 4x) × 9 = 126

➝ ½ × 7x × 9 = 126

➝ 7x = 126 × 2/9

➝ 7x = 252 /9

➝ 7x = 28

➝ x = 28/7

➝ x = 4

The sides become 3x = 3 × 4 = 12 & 4x = 4 × 4 = 16.

The lengths of smallest parallel side is 12 dm .

Answer 2

Answer:

\sf{\huge{\underline{\orange{Given :-}}}}

Given:−

The parallel sides of a trapezium are in the ratio 3 : 4.

The distance between the parallel sides is 9 dm .

The area of given trapezium is 126 dm².

\sf{\huge{\underline{\blue{To\:Find :-}}}}

ToFind:−

.

The lengths of smallest parallel side.

\sf{\huge{\underline{\green{Solution :-}}}}

Solution:−

Let the legth be in form of x,

The parallel sides of a trapezium are in the ratio 3 : 4.

Such that, 3x & 4x

The height is 9 dm

We know that the area of triangle,

➝ ½ × sum of || sides × height

➝ ½ × (3x + 4x) × 9 ------(1)

The area of given trapezium is 126 dm².------(2)

From Equation. 1 & 2

½ × (3x + 4x) × 9 = 126

➝ ½ × 7x × 9 = 126

➝ 7x = 126 × 2/9

➝ 7x = 252 /9

➝ 7x = 28

➝ x = 28/7

➝ x = 4

The sides become 3x = 3 × 4 = 12 & 4x = 4 × 4 = 16.

The lengths of smallest parallel side is 12 dm .