Question

meg.
The sides of a rectangular field are in the ratio 9.7 and its perimeter is 144 metres. Find the sides.
The sides of a rectangular piece of paper are in the ratio 2:3. If the area is 150 sq. cm, find the length
of its sides. (Hint: 52-25)
sides of a triangle are in the ratio 2.3:4 and its perim is 63 cm. What are the lengths of its​

Answer 1

Step-by-step explanation:

Given:

• Sides of a rectangular field are in ratio of 9:7
• Perimeter of rectangle is 144 m.

To Find:

• Measure of sides of rectangle?

Solution: Let x be the common in given ratio. Therefore,

➼ Length = 9x m

➼ Breadth = 7x m

As we know that

★ Perimeter of Rectangle = 2(Length + Breadth) ★

A/q

$\implies{\rm }$ 144 = 2(9x + 7x)

$\implies{\rm }$ 144 = 2(16x)

$\implies{\rm }$ 144 = 32x

$\implies{\rm }$ 144/32 = x

$\implies{\rm }$ 4.5 = x

So, Measure of sides are

• Length = 9x = 9(4.5) = 40.5 m

• Breadth = 7x = 7(4.5) = 31.5 m

____________________

Given:

• Sides of a rectangular piece of paper are in ratio of 2:3.
• Area of paper is 150 cm².

To Find:

• Measure of sides of paper ?

Solution: Let x be the common in given ratio. Then,

➼ Length of paper = 2x

➼ Breadth of paper = 3x

As we know that

★ Ar. of Rectangle = Length • Breadth ★

A/q

• area is 150 cm²

$\implies{\rm }$ 150 = 2x $\times$ 3x

$\implies{\rm }$ 150 = 6x²

$\implies{\rm }$ 150/6 = x²

$\implies{\rm }$ 25 = x²

$\implies{\rm }$ √25 = x

$\implies{\rm }$ √5 $\times$ 5 = x

$\implies{\rm }$ 5 = x

So, Measure of sides of rectangular paper are

• Length = 2x = 2(5) = 10 m

• Breadth = 3x = 3(5) = 15 m

___________________

Given:

• Sides of a triangle are in ratio of 2:3:4.
• Perimeter of triangle is 63 cm.

To Find:

• What is the length of its sides ?

Solution: Let x be the common in given ratio. So,

=> First side = 2x

=> Second side = 3x

=> Third side = 4x

As we know that

★ Perimeter of ∆ = Sum of all sides ★

A/q

• Perimeter is 63 cm

$\implies{\rm }$ 63 = 2x + 3x + 4x

$\implies{\rm }$ 63 = 9x

$\implies{\rm }$ 63/9 = x

$\implies{\rm }$ 7 = x

Hence, It's sides are

• First side = 2x = 2(7) = 14 cm.

• Second side = 3x = 3(7) = 21 cm.

• Third side = 4x = 4(7) = 28 cm.