Question

If the perimeter of a rectangle and a square, each is equal to $80$cm and the difference of their areas is $100$ sq cm, the sides of the rectangle are:

• A. 25 cm, 15 cm
• B. 28 cm, 12 cm
• C. 30 cm, 10 cm
• D. 35 cm, 15 cm

Answer 1

The correct option is C 30 cm, 10 cm

Perimeter of rectangle = perimeter of square $=80cm$

$\Rightarrow 2(l+b)=45=80$

$\Rightarrow S=\frac{80}{4}=20cm;2(l+b)=80$

$\Rightarrow l+b=40cm$ - $\left(1\right)$

difference $m$ areas $=100c{m}^2$

$5^2-\left(lb\right)=100$

$\left(20\right)\left(20\right)-\left(lb\right)=100$

$\Rightarrow lb=300$ - $\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$

$30+10=40;3\times 10=l\times b$

$\Rightarrow l=30$ and $b=10$

sides of rectangle are $30,10cm$