Question

the length of rectangle is four times its width . if its perimeter 120cm find its dimensions

Answer 1

let,
the length be 4x and the breadth be x.
Then,
2(4x+x)=120cm
8x+2x=120cm
10x=120
x=120/10
x=12cm
l=4x=4×12=48cm,b=12cm

Answer 2

The dimensions of the rectangle are length of 48 cm and a width of 12 cm when the length of a rectangle is four times its width. if its perimeter is 120 cm.

Formula used:

Perimeter of a rectangle, P = 2(length+ width)

P = 2(L + B)

Given:

The perimeter of a rectangle = 120 cm

Length = four times its width

To find: The dimensions of the rectangle

Solution:

Step 1: Let B be the Width of the rectangle and L be the length of the rectangle

According to the given conditions:

Perimeter of a rectangle =  2(L + W)

2(L + W)  = 120 …. (1)

Length is four times its width

L = 4B …….(2)

Step 2: Substituting the value of L from eq. 2 in eq.1 and solve:

2(L + B) = 120

$L + B = \frac{120}{2}$

L + B = 60

4B + B = 60

5B = 60

$B = \frac{60}{5}$

B = 12 cm

Width of a rectangle = 12 cm

Step 3: Substitute the value of B in eq. 2 :

L = 4B

L = 4(12)

L = 48 cm

Length of a rectangle = 48 cm

Hence the dimensions of the rectangle are length 48 cm and a width of 12 cm.

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