SOLUTION: The width of a rectangle is 5 feet, and the diagonal is 8 feet. Which is the area of the rectangle? (Round to nearest hundredth.)

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Question 425059: The width of a rectangle is 5 feet, and the diagonal is 8 feet. Which is the area of the rectangle? (Round to nearest hundredth.)
Answer by emargo19(101) About Me  (Show Source):
You can put this solution on YOUR website!
To find the area of the rectangle let use the pythogaras theorem, We are given the diagonal and the width of the rectangle. So this rectangle is divided into 2 right angled triangles(90 degrees each). Considering pythogoras theorem this diagonal is the hypothenuse, which is the longest side of the triangle while the width becomes one side of the triangle. Now let us use the pythogoras formula for finding the other side of the triangle.
The equation is c^2= a^2+b^2
where c= diagonal(hypothenuse)
a, b are the sides of the triangle.
So a= 5
Therefore
5%5E2%2B+b%5E2=8%5E2
25%2Bb%5E2=64
b%5E2=64-25
b%5E2=39
b=+6.244998
Now that we know the other side of the triangle which also happens to be the length of the rectangle. We can find the area of the rectangle using the formula
Area= Length * Width
Area=+5+%2A+6.244998
Area=+31.22499
Round it to the nearest hundred
Area=+31.225