The length of a rectangle is three times its width and the length of its diagonal is $610 cm$ . The perimeter of the rectangle is ____ cm.

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Detailed Solution

The length of a rectangle is three times its width and the length of its diagonal is

610 cm

. The perimeter of the rectangle is 48 cm.
Given the length of a rectangle is three times its width and the length of its diagonal is

610 cm

.
Let the width = x.
So, length = 3x.
Now, applying Pythagoras theorem,

(D i a g o n a l) 2 = (l e n g t h) 2 + (width) 2

(6 10) 2

(3 x) 2 + (x) 2

360 = 9 x 2 + x 2

360 = 10 x 2

x 2 = 36010

x 2 = 36

x = ± 6

Width = 6 cm
Length =

(3 × 6)

=18 cm
Perimeter = 2 (Length + Breadth)
= 2(18+6)
= 2(24)
= 48 cm
Perimeter of the rectangle is 48 cm.

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