The shorter side of a rectangle is 24 cm less than the longer side. The numerical value of its area is equal to 8 times the numerical value of its perimeter. What is the length (in cm) of its longer side?​

Correct option is B

Given:

Shorter side = Longer side − 24 cm

Area = 8 × Perimeter

Formula Used:

Area of rectangle = Length $$\times$$ breadth ​

Perimeter of rectangle = 2( length + breadth)

Solution: 

Let the longer side = x cm 

then shorter side = x - 24 cm 

Now, 

x(x - 24) = 8 $$\times 2$$​(x + x - 24) 

x(x - 24) = 8(4x - 48)

x² - 24x = 32x - 384

x² - 56x + 384 = 0 

x² - 48x - 8x + 384 = 0

x(x - 48) - 8(x - 48) = 0

(x - 8)(x - 48) = 0 

so, x = 8 or 48

But if x = 8, then shorter side = 8 - 24 = -16, which is not possible.

So, valid solution: x = 48 cm