SOLUTION: One of the legs of a right triangle has length √19 cm The sum of the lengths of the hypotenuse and the other leg is 19 cm. What is the area of this triangle in square centime

Algebra ->  Pythagorean-theorem -> SOLUTION: One of the legs of a right triangle has length √19 cm The sum of the lengths of the hypotenuse and the other leg is 19 cm. What is the area of this triangle in square centime      Log On


   

Question 355099: One of the legs of a right triangle has length √19 cm The sum of the lengths of the hypotenuse and the other leg is 19 cm. What is the area of this triangle in square centimeters?
Answer by robertb(5830) About Me  (Show Source):
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The legs have measure sqrt%2819%29 and b, the hypotenuse, c. We have to find the area A+=+b%2Asqrt%2819%29%2F2. It is given that b%2Bc+=+19, and so c+=+19-b. From the Pythagorean theorem, %28sqrt%2819%29%29%5E2%2Bb%5E2+=+c%5E2, or
19%2Bb%5E2+=+c%5E2.
By direct substitution,
19+%2B+b%5E2+=+%2819-b%29%5E2,
19+%2B+b%5E2+=+19%5E2+-+38b%2Bb%5E2,
19+=+19%5E2+-+38b,
38b+=+19%5E2+-+19,
2b+=+19+-+1, after dividing both sides by 19.
b+=+9. This area is then A+=9%2Asqrt%2819%29%2F2sq. cm.