Question 1048390: A rectangular room has area of 13.5m and diagonal of 6. What are the dimensions of the room?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The diagonal is a hypotenuse of a right triangle.
a^2+b^2=36
ab=13.5 sq m
a=13.5/b
now square it
a^2=182.25/b^2
substitute
[182.25/b^2]+b^2=36
multiply everything by b^2
182.25+b^4=36b^2
set equal to 0
b^4-36b^2+182.25=0
Treat like a quadratic, which means you can use the quadratic formula, only it is equal to b^2
b^2=(1/2)36+/- sqrt (1296-729))
b^2=(1/2)36+/- sqrt (567); sqrt (567)=23.81
b^2=(1/2)36+23.81=29.91; sqrt (29.91)=5.47m
b^2=(1/2)36-23.81=(6.10); sqrt 6.10=2.47m
5.47*2.47=13.51, rounding error. This checks. 5.47^2+2.47^2=29.9+6.10=36.
The room is 5.47 m x 2.47 m.
|
|
|
