Question

(a)The perimeter of a rectangle is 40 centimetres. length of its smaller side is 7 centimetres. what is length of its larger side ? (b) Find the side of the rectangle with perimeter 40 centimetres and area 96 square centimetres​

Answer 1

The answers are solved below:

(i) Given:

Perimeter of rectangle = 40 cm

Length of smaller side = a = 7 cm

To find:

Length of larger side = b

Solution:

$Perimeter\:of \:rectangle =2(a+b)$

$40 = 2\:(7+b)$

$20=7+b\\ b=20-7\\ b = 13 \:cm$

Answer: The length of its larger side is 13 cm.

(i) Given:

Perimeter of rectangle = 40 cm

Area of rectangle = A = 96 sq. cm

To find:

Side of rectangle = b

Solution:

$Perimeter\:of \:rectangle =2(a+b)$

$40 =2(a+b)$

$20 =a+b$

$b=20-a$

$Area\:of\:rectangle=ab$

$96=ab$

$96=a(20-a)$

$96=20a-a_{2}$

$a_{2}-20a+96=0$

Solving the above equation, the value of a can be 12 or 8.

Let value of a = 12 cm.

Then value of b = 20-12 = 8 cm

Answer: The sides of the rectangle are 12 cm and 8 cm.