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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:

✡ Question ✡

➡ The parallel sides of a trapezium are in the ratio 4:5. If the distance between the parallel sides is 6 cm and the area is 81 cm sq, find the lengths of the parallel sides of the trapezium.

✡ Given ✡

➡ The parallel sides of a trapezium are in the ratio 4:5.

➡The distance between the parallel sides is 6 cm and the area is 81 cm².

✡ To Find ✡

➡ The lengths of the parallel sides of the trapezium.

✡ Formula Used ✡

▶Area of trapezium = \dfrac{1}{2}

2

1

× (sum of parallel sides) × height

✡ Solution ✡

➡Let the parallel sides of the trapezium be 4x and 5x cm respectively.

Distance between the parallel sides = Height of the trapezium.

Then,

✴Height of the trapezium = 6 cm.

According to the question:-

=> \dfrac{1}{2}

2

1

× (4x + 5x) × 6 = 81

=> (4x + 5x) × 3 = 81

=> 9x × 3 = 81

=> 9x = \dfrac{81}{3}

3

81

=> 9x = 27

=> x = \dfrac{9}{27}

27

9

=> x = 3

∴ Length of the parallel sides of the trapezium,

4×3 = 12 cm

5×3 = 15 cm

Answer 2

Question:

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.

$\:$

Given:

• Ratio of 2 sides: 4:5
• h= 26 cm
• area of trapezium= 468 cm²

To find:

• Lengths of its parallel sides.

Solution:

$\tt \: AB||CD = 4:5$

$\tt \frac{AB}{CD} = \frac{4 \times x}{5 \times x} = \frac{4x}{5 x }$

As we know,

$\tt \qquad → \bold{Area \: trapezium}= {\bold \red{ \frac{1}{2} \times height× length \: of \: || \: sides }}$

$\tt \qquad → 468= \frac{1}{2} \times 26(4x + 5x)$

$\tt \qquad →468 = \frac{1}{2} \times 26 \times 9x$

$\tt \qquad →468 = 13(9x)$

$\tt \qquad →468 = 117x$

$\tt \qquad →4 = x$

Therefore,

$\sf \qquad →AB = 4x = 4 \times 4 = 16 {cm}^{2}$

$\sf\qquad → CD = 5x = 5 \times 4 = 20 {cm}^{2}$

• Length of parallel sides= 16 cm² and 20 cm².

$\bold \red{Celestial} \bold{Centrix}$