SOLUTION: Find the dimensions of a rectangle that has an area 48 m^2 and a diagonal of length 10 m.

Question 182199: Find the dimensions of a rectangle that has an area 48 m^2 and a diagonal of length 10 m.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let x = the length of the rectangle and y = the width of the rectangle.
The area is x*y = 48 sq.m.
The diagonal is 10 m, so from the Pythagorean theorem.
So we have two equations:
1) Rewrite this equation as: and substitute into equation 2).
2)
2a) Simplifying this, we get:
2a)
2a) Multiply both sides by
2a) Rearrange this into standard "quadratic" form.
Solve by factoring, noting that

Applying the zero product rule, we get:
or Factoring the left sides, we get:
or From which we get:

Discard the negative solutions as the lengths of the rectangle sides can only be positive.
So we have:
y = 6 or 8 and x = 8 or 6
The dimensions of the rectangle would be:
Length = 8m and width = 6m
Please note that while we solved only for y, the x-value is obtained by substituting y = 8 into eqation 1):
Substitute
Dividing both sides by 8.

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