SOLUTION: Find the perimeter and area of a right triangle if one leg measures 9 cm and the other leg measures 40 cm. Students must show all work step by step to receive full credit for the p

Algebra ->  Angles -> SOLUTION: Find the perimeter and area of a right triangle if one leg measures 9 cm and the other leg measures 40 cm. Students must show all work step by step to receive full credit for the p      Log On


   

Question 400347: Find the perimeter and area of a right triangle if one leg measures 9 cm and the other leg measures 40 cm. Students must show all work step by step to receive full credit for the problem. Include correct units with your solution.

Answer by Earlsdon(6294) About Me  (Show Source):
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If you are given the measure of the two legs of a right triangle, then you can find the length of the hypotenuse using the Pythagorean theorem.
Leg a = 9cm.
Leg b = 40cm.
Find c, the hypotenuse:
c%5E2+=+a%5E2%2Bb%5E2 or...
c+=+sqrt%28a%5E2%2Bb%5E2%29 Substitute a = 9 and b = 40.
c+=+sqrt%289%5E2%2B40%5E2%29 Square the inside numbers.
c+=+sqrt%2881%2B1600%29 Add.
c+=+sqrt%281681%29 Take the square root.
c+=+41
Find the perimeter, P:
P+=+a%2Bb%2Bc
P+=+9%2B40%2B41
P+=+90cm
To find the area, use:
A+=+%281%2F2%29b%2Ah where b = base (9cm) and h = height (40cm). Substitute.
A+=+%281%2F2%29%289%29%2840%29 Evaluate.
A+=+180sq.cm.