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.​

Answer 1

Answer:

The lengths of the parallel sides of the trapezium are 12 cm and 15 cm respectively.

Step-by-step explanation:

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 :-

• Lengths of parallel sides of the trapezium.

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.

★ Formula used :

${\boxed{\sf{Area\:of\: trapezium=\dfrac{1}{2}\times(sum\:of\: parallel\: sides)\times\: height}}}$

According to the question,

$\implies \sf \: \dfrac{1}{2} \times (4x + 5x) \times 6 = 81 \\ \\ \implies \sf \: (4x + 5x) \times 3 = 81 \\ \\ \implies \sf \: 9x \times 3 = 81 \\ \\ \implies \sf \: 9x = 27 \\ \\ \implies \sf \: x = \dfrac{27}{9} \\ \\ \implies \sf \: x = 3$

Therefore,

Length of the parallel sides of the trapezium,

• 4×3 = 12 cm
• 5×3 = 15 cm

Answer 2

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 = $\dfrac{1}{2}$ × (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:-

=> $\dfrac{1}{2}$ × (4x + 5x) × 6 = 81

=> (4x + 5x) × 3 = 81

=> 9x × 3 = 81

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

=> 9x = 27

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

=> x = 3

∴ Length of the parallel sides of the trapezium,

4×3 = $\bold{\large{\fbox{\color{blue} {12 cm}}}}$

5×3 = $\bold{\large{\fbox{\color{blue} {15 cm}}}}$

Step-by-step explanation:

HOPE IT HELP YOU