Question

The length of a rectangle is three time its width and the of its diagonal is 6 root under 10 perimeter of the rectangle is

Answer 1

Step by step :-

Suppose value of width ( breath ) is equal to

$= x$

Than, value of length is three times of breath.

$= 3x$

Diagonal is hypotenuse of right triangle which sides are length and breath.

${(x)}^{2} + {(3x)}^{2} = 6 \sqrt{10} \\ {x}^{2} + {9x}^{2} = 6 \sqrt{10} \\ 10 {x}^{2} = 6 \sqrt{10} \\ {x}^{2} = \frac{6 \sqrt{10} }{10} \\ x = \sqrt{ \frac{6 \sqrt{10} }{10} } \\ x = \frac{ \sqrt{6 } \times 10 }{ \sqrt{10} }$

Answer 2

let the width of rectangle be x

the length of rectange is 3x

Therefore,

by Pythagoras theorem

(6root under 10)sq = x sq + (3x)sq

(6root under 10)sq = x sq +9x sq

(6root under 10)sq =10x sq

36×10=10x sq

10x sq=36 × 10

x sq=36

x =under root 36

x= 6 cm

Therefore,

The width of rectangle = 6

The length of rectangle = 6×3

=18

Therefore Now,

The perimeter of rectangle = 2(length + width)

=2(6+18)

=2×24

=48 cm

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