Question

The perimeter of a rectangle is 52 cm. If its width 2 cm more than one third of its length. Find the area of rectangle

Answer 1

Solutions :-

Given : Perimeter of a rectangle = 52 cm

Let the Length be x

So, Breadth = 1/3 x + 2 cm

We know,

Perimeter of rectangle = 2 (Length + Breadth )

A/q

➠ 2 (x+1/3x+2) = 52

➠ 2 (4x/3+2) = 52

➠ 2 ((4x+6)/3) = 52

➠ (8x+12)/3 = 52

➠ 8x+12 = 52×3  

➠ 8x+12 = 156

➠ 8x = 156 - 12

➠ 8x = 144

➠ x = 144/8 ➠ 18

Length = x = 18 cm

Breadth = 1/3 x + 2 cm = ((1×18)/3 + 2)cm = 8 cm

Now,

Find the area of rectangle :-

Area of rectangle = (Length × Breadth) sq. Unit

= (18 × 8) cm²

= 144 cm²

Hence,

Area of rectangle is 144 cm²