Question 792477: how to find the length and the width of the rectangle if the diagonal is 7
Answer by harpazo(655)   (Show Source):
You can put this solution on YOUR website! Use the Pythagorean Theorem.
Let x represent the length and width. If x represents the length and width, this means that your shape is actually a square NOT a rectangle. Why? Because a square has EQUAL MEASURE on all four sides.
Let d represent the diagonal.
x^2 + x^2 = d^2
2x^2 = 7^2
2x^2 = 49
x^2 = 49/2
sqrt{x^2} = sqrt{49/2}
x = 7/sqrt{2}
You may rationalize the denominator. If you do, the answer for x is
7(sqrt{2})/2. This is the measure of the length and width, which means this figure is actually a square not a rectangle.
How do we read 7(sqrt{2})/2?
The length and width is 7 times the square root of 2 divided by 2.
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