Question

The ratio of two adjacent sides of a parallelogram is 2:3.Its perimeter is 50 cm. Find its area if altitude corresponding to larger side is 10 cm.

Answer 1

Let the sides be 2x cm & 3x cm

We know,

Perimeter of Parallelogram

= 2 × Sum of Adjacent sides

According to Question,

Perimeter of Parallelogram = 50 cm

2(2x + 3x) = 50

⇒ 5x = 50 / 2

⇒ 5x = 25

⇒ x = 25 / 5

⇒ x = 5

Required Adjacent Sides »

One Side = 2x = 2(5) = 10 cm

Another Side = 3x = 3(5) = 15 cm

Clearly, 15 cm > 10 cm

Hence, 15 cm is the larger side or Base of the parallelogram.

Corresponding Altitude = 10 cm

Area of Parallelogram

= (Base × Altitude) Square Units

= (15 × 10) cm²

= 150 cm²

Hence, the area of Parallelogram is 150cm².

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Answer 2

Dear friend,

Here's your answer...

Let the sides be 2x and 3x.

As two opposite sides of a //gm are equal and parallel, so the four sides are 2x ,3x ,2x and 3x.

Perimeter of //gm = Sum of all sides

50 = 2x + 3x + 2x + 3x

50 = 10x

5 = x

So, the sides are 2x = 2×5 = 10cm = 2x = 10 cm

3x = 3×5 = 15cm = 3x = 15 cm

The longer side is 15 cm and its altitude is 10 cm.

Therefore the area of the //gm = b × h

= 15 × 10 = 150cm²

Hope its right and helpful for you !!