Question

The diagonal of a rectangular room is 1313 ft long. One wall measures 77 ft longer than the adjacent wall. Find the dimensions of the room. The shorter wall of the room is nothing ft.

Answer 1

The room is 996.13 ft by 889.13 ft

Step-by-step explanation:

let AC = x

AB = 77+x

BC = 1313

Therefore using Pythagoras theorem, we get

`(BC)^(2) = (AB)^(2)+(AC)^(2)`

`(1313)^(2) = (77+x)^(2)+(x)^(2)`

`1723969 = (77)^(2)+2* 77* x+x^(2)+x^(2)`

`1723969 = 5929+154x+2x^(2)`

`1718040 =154x+2x^(2)`

`2x^(2)+154x-1718040=0`

`x^(2)+77x-859020=0`

Therefore on solving, we get

x = 889.13 ft

∴ The dimension of the rectangular room is

AC = x = 889.13 ft

AB = 77+x = 77+ 889.13 = 996.13 ft

Therefore the room is 996.13 ft by 889.13 ft