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Find the perimeter of the rectangle whos...

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

A

`97cm`

B

`89cm`

C

`98cm`

D

`88cm`

Text Solution

Verified by Experts

The correct Answer is:
C
We can create a rectangle `ABCD` with the given details.
One side of rectangle `AB = 40 cm`
Diagonal of rectangle `AC = 41 cm`
So, other side of rectangle, `BC = sqrt(41^2-40^2)cm`
`BC = sqrt(1681-1600) = sqrt81 = 9cm`
So, Perimeter of rectangle `ABCD`, `P = 2**(AB+BC)`
`P = 2**(40+9) = 2**49 = 98cm`
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