Question

The perimeter of rectangle is $140$ cm. If the sides are in the ratio $3:4$, find the lengths of the four sides and the two diagonals

• A. Sides $=30cm,40cm$, Diagonal $=50cm$
• B. Sides $=30cm,40cm,$ Diagonal $=100cm$
• C. Sides $=60cm,80cm$, Diagonal $=100cm$
• D. none of the above

Answer 1

The correct option is A Sides $=30cm,40cm$, Diagonal $=50cm$

Given: Perimeter of Rectangle $=140cm$

Ratio of sides $=3:4$, so let $length=4x,$ $breadth=3x$

Perimeter of Rectangle $=2(l+b)$

$\therefore 2(4x+3x)=140$

$7x=70$

$x=10$

$\therefore length=40,$ $breadth=30$

$\therefore \text{sides of rectangle}=30cm,40cm$

Diagonal of Rectangle $=\sqrt{l^2+b^2}$ (by pythahoras theorem)

$=\sqrt{{30}^2+{40}^2}$

$=\sqrt{2500}$

$=50cm$