Question

Open area of a house is in the shape of a trapezium with parallel sides in the ratio 3 : 5. Its area is 80 m² and the perpendicular distance between the parallel sides is 5 m. Find the length of two parallel sides of that open area.​

Answer 1

Answer:

Given:

The open area of a house is in the shape of a trapezium with parallel sides in the ratio 3:5.

Its area of 50 m² and the perpendicular distance between the parallel sides is 5m

To find:

Find the length of two parallel sides of the open area.

Solution:

Let's assume "3x" & "5x" are two parallel sides of the trapezium-shaped open area of the house.

The area of the trapezium-shaped open area = 50 m²

The perpendicular distance between the parallel sides i.e., h = 5m

We know the formula of the area of a trapezium is as follows:

Now, on substituting the given values in the formula above, we get

∴ 3x = 3 × 2.5 = 7.5 m

∴ 5x = 5 × 2.5 = 12.5 m

Thus, the length of two parallel sides of the open area of the house is → 7.5 m and 12. 5 m.

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Also View:

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Find the area of the trapezium whose parallel sides are 14cm and  10cm and whose height is 6cm.​

 

The area of a Trapezium is 98 CM square and its height 7 cm if one of the parallel side 6 CM longer than the other find the length of the parallel side​

Step-by-step explanation:

Answer 2

Answer:

Given:

The open area of a house is in the shape of a trapezium with parallel sides in the ratio 3:5.

Its area of 50 m² and the perpendicular distance between the parallel sides is 5m

To find:

Find the length of two parallel sides of the open area.

Solution:

Let's assume "3x" & "5x" are two parallel sides of the trapezium-shaped open area of the house.

The area of the trapezium-shaped open area = 50 m²

The perpendicular distance between the parallel sides i.e., h = 5m

We know the formula of the area of a trapezium is as follows:

$\boxed{\bold{Area\:of\:a\:trapezium = \frac{1}{2} \times (sum\:of\:parallel\:sides)\times (perpendicular \:distance)}}$

Now, on substituting the given values in the formula above, we get

$50 = \frac{1}{2} \times (3x + 5x)\times (5)}}$

$\implies 50 = \frac{1}{2} \times (8x )$

\implies 50 = 4x\times 5⟹50=4x×5

$\implies 50 = 4x\times 5$

$\implies 50 = 20x$

$⟹50=20x$

$\implies x = \frac{50}{20}$

$\implies \bold{x = 2.5}$

∴ 3x = 3 × 2.5 = 7.5 m

∴ 5x = 5 × 2.5 = 12.5 m

Thus, the length of two parallel sides of the open area of the house is → 7.5 m and 12. 5 m.