Question - Solving the Length of the Hypotenuse in an Isosceles Right Triangle
Solution:
The image shows a right triangle with one angle marked as 45 degrees, which means it is an isosceles right triangle (since the other non-right angle must also be 45 degrees). In such triangles, the legs are congruent. If the triangle is labeled with points G, J, and H, where GH is the hypotenuse, and the leg GJ is labeled as "4√2," then we can find the length of GH using the Pythagorean theorem. However, for an isosceles right triangle, we have a simpler relationship:In an isosceles right triangle, the length of the hypotenuse is √2 times the length of a leg.Given GJ = 4√2, the length of GH (the hypotenuse) is:GH = GJ * √2GH = 4√2 * √2GH = 4 * (√2 * √2)GH = 4 * 2GH = 8Therefore, the exact value of GH is 8, which corresponds to option C.
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