Question

Mrs.Kaushik gives a problem to her students. Find the perimeter of a rectangle whose length is $28cm$ and diagonal is $35cm$. What will be the correct answer?

• A. $90cm$
• B. $45cm$
• C. $89cm$
• D. $98cm$

Answer 1

Answer: (D)

$98cm$

$ABCD$ is a rectangle
In $△ACB,{AC}^2={AB}^2+{BC}^2$
(By pythagoras theorem)
${\left(35\right)}^2={\left(28\right)}^2+{BC}^2\Rightarrow {BC}^2={\left(35\right)}^2-{\left(28\right)}^2$
$\Rightarrow {BC}^2=1225-784=441$
$\Rightarrow BC=\sqrt{441}=21cm$
Perimeter of rectangle $=2\times (28\times 21)cm=98cm$