Question

Two plots have the same perimeter. One is a square of side 10 m and another is a rectangle of breadth 8 m. Which plot has the greater area and by how much?

Answer 1

Given perimeter of square = perimeter of rectangle

4 × side = 2(length + breadth)

(4 × 10) m = 2(l + 8) m

`(4 xx 10)/2` = l + 8

20 = l + 8

l = 20 – 8

l = 12 m

∴ length of the rectangle = 12 m

Area of the square plot

= side × side

= 10 × 10 m² 

= 100 m²

Area of the rectangular plot

= length × breadth

= (12 × 8) m² 

= 96 m²

100 m² > 96 m²

∴ Square plot has greater area by 4m²