Question

The perimeter of a rectangle is $28$ cm and one of its sides is $8$ cm long. What is the length of the diagonal of the rectangle?

• A. $6$ cm
• B. $10$ cm
• C. $16$ cm
• D. $14$ cm

Answer 1

The correct option is B $10$ cm


Here $ABCD$ is the rectangle having side $AB=8$ cm and perimeter $28$ cm now we have to find out the value of $AC$.

We know, opposite sides of the rectangle are equal.
So $AB=CD=8cmandBC=AD=x$
Perimeter=$AB+BC+CD+DA$
$28=8+8+x+x$
$28=16+2x$
$12=2x$
$x=6$ cm

Hence, side $BC=AD=6$ cm

Now, in $△ABC$ right angled at $\angle B$
applying pythagoras theorem,
$A{B}^2+B{C}^2=A{C}^2$
$A{C}^2=8^2+6^2$
$A{C}^2=64+36$
$A{C}^2=100$
$AC=\sqrt{100}=10$ cm

Hence, length of the diagonal is $10$ cm. so option $\left(b\right)$ correct.