Question

The area of a rectangle is 768 sq cm if the length and breath are in ratio of 4:3 find length ,breath , and perimeter

Answer 1

Q. The area of a rectangle is 768 cm². If the length and breadth are in the ratio of 4:3 find the length, breadth and perimeter.

Solution :

Given :
area of the rectangle = 768 cm²
ratio of length and breadth = 4:3

Let,
length = 4x cm
breadth = 3x cm

We know that,
Area of rectangle = length*breadth

=> 768 = 4x*3x

=> 768 = 12x²

=> 768/12 = x²

=> 64 = x²

=> √64 = x

=> 8 = x

Hence, the value of x = 8

Now,
length = 4x = 4*8 = 32 cm
breadth = 3x = 3*8 = 24 cm

Perimeter of rectangle = 2 (l +b)
[ in which 'l' is the "length" and 'b' is the "breadth" ]

Perimeter of the rectangle = 2 (32+24)
= 2*56
= 112

Hence, perimeter of rectangle = 112 cm.

Answer 2

Given length:breadth = 4:3
Let length = 4x and breadth = 3x
Diagonal = 25 cm
Since the diagonal and the two adjacent sides of a rectangle form a right angled triangle
By Pythagoras theorem, we have
252 = (4x)2 + (3x)2
625 = 16x2 + 9x2 = 25x2
⇒ x2 = 25
∴ x = 5
Hence length = 4x = 20 m and breadth = 3x = 15 m
Perimeter of rectangle = 2(length + breadth)
                                    = 2(20+15) = 70 m