Question

the perimeter of a rectangle is 40 cm. if its length is 3 times its width, then its diagonal is equal to

Answer 1

Let the width be x cm
So height is 3x cm.
2(x+3x)=40
8x=40
x=40/8
x=5

Diagonal²=height²+width²
                =(3x)²+x²
                =9x²+x²
                =10(5)²
Diagonal=√250
              =5√10 cm

The diagonal is 5√10 cm

Answer 2

Hey friend, Harish  here.

Here is your answer:

Given that,

Perimeter = 40cm.

Length = 3 × width.

To find,

The Diagonal of the rectangle.

Solution,

Let Width b ' x ' .Then Length is 3 × x ⇒ 3x.

Then,

We know that,

[tex]Perimeter= 2(Length+Width) [/tex]

⇒  $40= 2 ( 3x+x)$

⇒  $40 = 2(4x)$

⇒  $40 = 8x$

⇒  $x = \frac{40}{8}=5$

Therefore width = x = 5cm,

                 Length = 3x = 3 × 5 = 15cm.

We also know that,

$Diagonal = \sqrt{(Length)^{2}+(Width)^{2}} = \sqrt{(15)^{2}+5^{2}} = \sqrt{5^{2}(3^{2}+1)}$

⇒  $5( \sqrt{3^{2}+1}) = 5 \sqrt{10}\ cm$

Therefore Diagonal length is 5√10 cm.
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Hope my answer is helpful to you