SOLUTION: The area of a rectangle is the square root of 3m^2 and the length of a diagonal is 2m. Find its dissensions

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The area of a rectangle is the square root of 3m^2 and the length of a diagonal is 2m. Find its dissensions      Log On


   



Question 1194281: The area of a rectangle is the square root of 3m^2 and the length of a diagonal is 2m. Find its dissensions
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
x, y, the dimensions
system%28xy=sqrt%283%29%2Csqrt%28x%5E2%2By%5E2%29=2%29
.
.
.
I have not tried to solve this thoroughly, but ...
y^2+x^2=4
y^2=4-x^2


x^2*y^2=3
therefore
x^2*(4-x^2)=3, one equation in just one unknown variable


-------------
-------------

-x%5E4%2B4x%5E2-3=0
x%5E4-4x%5E2%2B3=0
u=x%5E2
THEN
u%5E2-4u%2B3=0
%28u-1%29%28u-3%29=0
u=1 OR u=3

.
.
.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let one dimension of the rectangle be x.

Then, since the area is sqrt%283%29, the other dimension is sqrt%283%29%2Fx.

The diagonal has length 2, so the square of the diagonal is 4.

x%5E2%2B%28sqrt%283%29%2Fx%29%5E2=4
x%5E2%2B3%2Fx%5E2=4
x%5E2-4%2B3%2Fx%5E2=0
x%5E4-4x%5E2%2B3=0
%28x%5E2-1%29%28x%5E2-3%29=0

x=1 or x=sqrt%283%29 (ignore the negative solutions, since they make no sense)

If x is 1, then the other dimension is sqrt(3); if x is sqrt(3), then the other dimension is 1. Either way, the dimensions of the rectangle are 1 and sqrt(3).

ANSWER: 1 by sqrt(3)