Question

What will be the perimeter of a rectangle if its length is 3 times its width and the length of the diagonal is $8\sqrt{10}$ cm ?

• A. $16\sqrt{10}$ cm
• B. $15\sqrt{10}$ cm
• C. $64$ cm
• D. $24\sqrt{10}$ cm

Answer 1

The correct option is C $64$ cm

Let length$=lcm,$ width$=bcm$

$\Rightarrow l=3b$,Diagonal$=8\sqrt{10}cm$

Now, $l^2+b^2=d^2\Rightarrow {\left(3b\right)}^2+b^2{\left(8\sqrt{10}\right)}^2\Rightarrow 10b^2=640$

$\Rightarrow b^2=64\Rightarrow b=\sqrt{64}=8cm$ & $l=3b=3\times 6=24cm$

Perimeter$=2(l+b)=2(24+8)=64cm$