Question

If the perimeter of a rectangle is 44 cm and the area is 120 square cm, then what are the dimensions of the rectangle?

Answer 1

length =12 cm and breadth= 10 cm

Explanation:

we know that perimeter of a rectangle is 2*(l+b) and area of a rectangle is l*b.

2*(l+b)= 44 cm and l*b=120 sq.cm

2l+2b= 44cm l*b=120sq.cm

lets take out all the factors of 120 as this may help in finding l and b.

1,2,3,4,5,6,8,10, 12,15,20,24,30,40,60,120.

here, the most likely answer that verifies that l and b can be found is using the perimeter.

so, out of all these factors, 10 and 12 gives the right answer to 2*l+b

2* 10+12=2*22=44 cm and it also satisfies l*b as 10*12 is 120...

Answer 2

Explanation:

Perimeter of rectangle = 44 cm

2*(length +width) = 44

l = length

w = width

2*( l +w) =44

Divide both sides by two

l +w = 44/2

l +w = 22

l = 22 - w ----------------------(I)

Area of rectangle= 120 square cm

l * w = 120

(22 - w) *w = 120 {from(I)}

22w - w² = 120

0 = 120 - 22w +w²

w² - 22w + 120 = 0

Sum = - 22

Product = 120

Factors = -12 , -10

w² - 22w + 120 = 0

w² - 12w - 10w + (-12)*(-10) = 0

w(w - 12) -10 (w -12) = 0

(w - 12)(w - 10) = 0

w -12 = 0 ;w - 10 = 0

w = 12 ; w = 10

Dimension of rectangle are: 12 , 10