SOLUTION: Find the area of a rectangle if the length of one of its sides is 9it meters and the length of its diagonals is 13 meters

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Question 848409: Find the area of a rectangle if the length of one of its sides is 9it meters and the length of its diagonals is 13
meters
Answer by pmesler(52) About Me  (Show Source):
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To find the area of a rectangle we need to know the width and length of the rectangle. We know that the length is 9 meters. To find the width we need to apply what we know about right triangles.
Start out by drawing a rectangle. Then draw a diagonal through the rectangle. As you can see, you've created two right triangles. The diagonal is the hypotenuse to both triangles.
The length of the rectangle is the base to the new right triangle. We know the diagonal or hypotenuse is 13 meters. Therefore by applying the Pythagorean Theorem we get
a^2 + 9^2 = 13^2. Now solve for a to find the width.


a^2 + 81 = 169
Subtract 81 from both sides.

a^2 = 88
Take the square root of both sides.
a = 9.38 or 9.4 meters.
Therefore the area of the rectangle is
A = W * L
A = 9.4 * 9
A = 84.43 meters squared.