SOLUTION: What is the area of a right triangle with a hypotenuse measuring 5 inches and a base measuring 4 inches?

Question 633396: What is the area of a right triangle with a hypotenuse measuring 5 inches and a base measuring 4 inches?

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
This is a very common size for a right triangle. If a right triangle has a hypotenuse of 5 and one of its legs is 4, then the other leg is 3. Other than knowing this, you can find the unknown leg by using the Pythagorean theorem. It says that the square of the hypotenuse (in this case 5) equals the sum of the squares of the two legs. One of the legs in this case is known to be 4 and the other leg is unknown. Call this unknown leg A. So we can write:
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Square the two numbers and this equation becomes:
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Subtract 16 from both sides of the equation to reduce it to:
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Solve for A by taking the square root of both sides and you have:
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So now you know all three sides are 3, 4, and 5 in which the hypotenuse (or longest side) is 5.
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This means that the base (given in the problem) is 4 and the perpendicular to it (the altitude in a right triangle) is the leg that you found to be 3.
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The area of a triangle is 1/2 times the base times the altitude. So the area of this triangle is:
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Find the area by multiplying the three numbers on the right side to get:
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And don't forget to add the units of square inches since the problem said that the two given sides in the triangle had units of inches.
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Hope this helps you to understand the problem.
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