Question

Two plots of land have the same perimeter. One is a square of side $60m$, while the other is a rectangle whose breadth is $1.5$ dam. Which plot has the greatest area and by how much?

• A. Rectangle, $32m^2$
• B. Rectangle, $36m^2$
• C. Square, $32m^2$
• D. Square, $36m^2$

Answer 1

The correct option is D Square, $36m^2$

Length of the square $=64$ m

Length of the rectangle $=70$ m

Perimeter of the square $=4\times \text{side}=4\times 64=256$ m

Let breadth of the rectangle $=B$

Perimeter of the rectangle $=2(70+B)$

Now, according to question,

$2\times (70+B)=256$

$\Rightarrow 140+2B=256$

$\Rightarrow 2B=256-140$

$\Rightarrow 2B=116$

$\Rightarrow B=58$ m

Area of the rectangle $=58\times 70=4060$ sq. m

Area of the square $=$ length $\times$ breadth $=64\times 64=4096$ sq.m

Square has more area by $36$ sq. m.