Question 332782: A rectangle is 24 cm long and 10 cm wide. Its diagonal is labeled 4x - 2. What is the value of x?
Answer by Jstrasner(112)   (Show Source):
You can put this solution on YOUR website! Hey,
So for this problem, we simply need to picture it. There is a rectangle with a diagonal. A rectangle is the same as two triangles with the diagonal serving as the hypotenuse. Therefore, if we take one triangle out, its dimmensions are 10 cm for one base, 24 cm for another base, and for the hypostenuse is 4x-2. To find what 4x-2 is equal to we use the pythagorean theorem: a^2 + b^2 = c^2, where a and b are the bases and c is the hypotenuse. Therefore:
24^2 + 10^2 = c^2
676 = c^2
26 = c
So 26 = 4x-2
Therefore: we add 2 to both sides and we get : 28 = 4x and we find that x equals to 7.
I hope this helps!
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