Question

1. The sides of a rectangle are in the ratio 8:7 and its perimeter is 90 cm. The length of
the rectangle is
(a21 cm
(b) 24 cm
(c) 32 cm
(d) 28 cm
​

Answer 1

Answer :-

• The correct option is b)
• The length of the rectangle is 24 cm.

Given :-

• The sides of a rectangle are in the ratio 8 : 7.
• Its perimeter is 90 cm.

To find :-

• The length of the rectangle.

Step-by-step explanation :-

Since the sides are in the ratio 8 : 7,

Therefore let the length be 8x and the breadth be 7x.

We know that :-

Perimeter of a rectangle = 2 (Length + Breadth).

The perimeter is 90 cm.

So, applying this formula,

$\sf 2 \: (8x + 7x) = 90 \: cm$

$\sf 16x + 14x = 90 \: cm$

$\sf 30x = 90 \: cm$

$\sf x = \dfrac{90 \: cm}{30}$

$\sf x = 3 \: cm$

The value of x is 3.

Therefore, the length and breadth are as follows :-

Length = 8x = 8 × 3 cm = 24 cm.

Breadth = 7x = 7 × 3 cm = 21 cm.

________________________________

Verification :-

To check our answer, lets put the value of the length and breadth and see if we get 90 cm (Perimeter).

Substituting the values,

$\sf 2 \: (24 \: cm + 21 \: cm) = 90 \: cm$

$\sf 48 \: cm + 42 \: cm = 90 \: cm$

$\sf 90 \: cm = 90 \: cm$

Since the length and breadth is equal to the perimeter,

Hence verified! ✔️✔️

Answer 2

Answer:

90cm=90cm hence proved