Question

. The sides of rectangle are in the ratio 5:4 and its
perimeter is 90 cm. Find its length & breath.( please answer it quickly)​

Answer 1

ANSWER :

• ❖ If the sides of rectangle are in the ratio 5:4 and its perimeter is 90 cm, then the length of the rectangle is 25 cm and breadth of the rectangle is 20 cm.

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SOLUTION :

❍ Given :-

• Ratio of the sides of the rectangle = 5 : 4

• Perimeter of the rectangle = 90 cm

❍ To Find :-

• Length of the rectangle = ?

• Breadth of the rectangle = ?

❍ Required Formula :-

• $\boxed{\bold{\: Perimeter \: \: of \: \: a \: \: rectangle = 2 \: (Length + Breadth) \:}}$

❍ Calculation :-

Suppose,

• Length of the rectangle = 5x

• Breadth of the rectangle = 4x

Using the formula of Perimeter of a rectangle, we get,

• Perimeter of the rectangle = 2 ( Length + Breadth)

⟹ Perimeter of the rectangle = 2 (5x + 4x)

According to question,

• Perimeter of the rectangle = 90

➨ 2 (5x + 4x) = 90

➨ 5x + 4x = $\dfrac{90}{2}$

➨ 9x = 45

➨ x = $\dfrac{45}{9}$

∴ x = 5 ★

Substituting the value of x, we get,

• ❖ Length of the rectangle = 5x = (5 × 5) cm = 25 cm

• ❖ Breadth of the rectangle = 4x = (4 × 5) cm = 20 cm

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VERIFICATION :

❍ We have :-

• Length of the rectangle = 25 cm

• Breadth of the rectangle = 20 cm

• Perimeter of the rectangle = 90 cm

❍ To Verify :-

• 2 (Length + Breadth) = Perimeter

Now,

• L.H.S. = 2 (Length + Breadth)

= {2 × (25 + 20)} cm

= (2 × 45) cm

= 90 cm

And,

• R.H.S. = Perimeter

= 90 cm

∴ L.H.S. = R.H.S. ★

• Hence, Verified.