The shorter side of a rectangle is 21 cm less than the longer side. The numerical value of its area is equal to 5 times the numerical value of its perimeter. What is the length (in cm) of its longer side?​

Correct option is C

Given:

The shorter side of a rectangle is 21 cm less than the longer side

The area of the rectangle is equal to five times the perimeter

Formula Used:

Area of rectangle = Length × Width

Perimeter of rectangle = 2(Length + Width)

Solution: 

Let the longer side be x cm, and the shorter side be x - 21 cm

Now, 

Area of the rectangle = x(x - 21) = x² - 21x

Perimeter = 2(x + (x - 21)) = 2(2x - 21) = 4x - 42

So, 

x² - 21x = 5(4x - 42)

x² - 21x = 20x - 210

x² - 41x + 210 = 0

(x - 35)(x - 6) = 0 

x = 35 and 6 

Since the longer side must be larger than the shorter side, x = 35

Thus, the length of the longer side is 35 cm