Question

In trapezium PQRS PQ || RS and the ratio of PQ to S R is 3:2. If the area of trapezium is 48 cm^2 and the distance between PQ and SR is 12cm then the length of the SR is?
36cm
48cm
24cm
32cm​

Answer 1

Given

• Trapezium PQRS
• PQ || RS
• Ratio of PQ to SR → 3:2
• Area of trapezium → 48 cm²
• Distance between PQ and SR → 12 cm

___________________________

To Find

• The length of SR

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Solution

So we know that PQ and RS and parallel sides of the trapezium and are in the ratio of 3:2.

So let's consider PQ as 3x and RS as 2x

Distance between PQ and RS → 12 cm

Area of trapezium → 48 cm²

Formula to find the area of trapezium → $\sf \dfrac{Side\ 1 + Side \ 2}{2} \times Height$

Let's solve the below equation to find the value of each side of the trapezium.

$\dfrac{3x+2x}{2}\times 12 = 48$

Step 1: Simplify the equation.

⇒ $\dfrac{3x+2x}{2}\times 12 = 48$

⇒ $\dfrac{5x}{2}\times 12 = 48$

⇒ $5x \times 6 = 48$

Step 2: Divide 6 from both sides of the equation.

⇒ $5x \times 6\div 6 = 48\div 6$

⇒ $5x = 8$

Step 3: Divide 5 from both sides of the equation.

⇒ $5x\div 5 = 8\div 5$

⇒ $x = 1.6$

∴ The length of PQ → 3x = 3(1.6) = 4.8 cm

∴ The length of SR → 2x = 2(1.6) = 3.2 cm

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Answer 2

Answer:

Given :-

Trapezium PQRS

PQ || RS

Ratio of PQ to SR => 3:2

Area of trapezium => 48 cm²

Distance between PQ and SR => 12 cm

To Find :-

Length of SR

Solution :-

At first let's assume

PQ = 3a

SR = 2a

Now,

We know that

Area = ½(a + b) × h

Here,

a + b = 3a + 2a

h = 12

48 = ½(3a + 2a) × 12

48 = 6(5a)

48/6 = 5a

8 = 5a

8/5 = a

1.6 = a

Now

SR = 2(1.6) = 3.2 cm