A rectangle has 15 cm as its length and 150 $$cm^2$$​ as its area. If the area is increased to $$1 \frac{1}{3}$$​ times the original area by increasing its length only, then the new perimeter is:​

Correct option is B

Given:

Length of the rectangle (L) = 15 cm

Area of the rectangle (A) = 150$$cm^2$$ 

​New area = $$1\frac{1}{3}$$ times the original area 

Formula Used: ​

Area of Rectangle = Length $$\times$$ Breadth

Perimeter of Rectangle = 2(Length + Breadth)

Solution:

A = L × B 

150 = 15 × B 

​$$B = \frac{150}{15}$$ 

B = 10cm 

The new area:

New area = $$1 \frac{1}{3} \times 150$$ 

​New area = $$\frac{4}{3} \times 150$$ 

​New area = 200 $$cm^2$$ 

The new length (l) using the new area while keeping the same breadth (10 cm)

200  = l × 10

​$$l= \frac{200}{10}$$ = 20 cm

The perimeter of the new rectangle:

Perimeter = 2 × (L + B)

Perimeter = 2 × (20 + 10) 

Perimeter = 2 × 30 

Perimeter = 60cm 

The new perimeter of the rectangle is 60 cm​