If the perimeter of a certain rectangle is 76 and its area 360, then what is the length of its shortest side?

Formula Used:

Perimeter of rectangle = 2[Length + Breadth]

Area of rectangle = Length × Breadth 

Calculation:

Using above formula -

⇒ 2[L + B] = 76

⇒ L + B = 38                               ...(1)

Area of rectangle is 360

⇒ L × B = 360                              ...(2)

Using (1) & (2)

⇒ L(38 - L) = 360

⇒ 38L - L² = 360

⇒ L² - 38L + 360 = 0

⇒ L² - 18L - 20L + 360 = 0

⇒ L(L - 18) - 20(L - 18) = 0

⇒ (L - 18)(L - 20) = 0

⇒ L = 18 or 20 units

If L = 18 Units ,B = 38 - 18 = 20 Unit

If L = 20 Units ,B = 38 - 20 = 18 Unit

∴ The correct answer is 18 unit