Question

A rectangle is 16 m by 9 m. Find a side of the square whose area equals the area of the rectangle . By how much does the perimeter of the rectangle exceed the perimeter of the square

Answer 1

Hey

Given that :-

• Lenght if rectangle = 16 m

• Breadth of rectangle = 9 m

So ,

area of rectangle = l* b

= 16 * 9

= 144 m² .

Now ,

area of rect = area of square

So ,

Area of square = 144 m²

=> a ² = 144

=> a = √ 144

=> a = √ 12 * 12

=> a = 12 .

So , side of square = 12 m .

Now ,

Perimeter of rectangle

= 2 * ( l + b )

= 2 * ( 16 + 9 )

= 2 * 25

= 50 m

And ,

Perimeter of square

= 4 * a side

= 4 * 12

= 48 m

So , perimeter of rectangle is more that that of square by ( 50 - 48 ) m = 2 m

thanks :)

Answer 2

Area of rectangle = (16 × 9) m2 = 144 m2

Given condition,

Area of square = Area of rectangle

∴ (Side)2 = 144

Side = √144 = 12 m

Now,

Perimeter of square = 4 × side = 4 × 12 = 48 m

Perimeter of rectangle = 2(l + b) = 2 (16 + 9) = 50 m

Hence, difference in their perimeters = 50 – 48 = 2 m