SOLUTION: Perimeter of right angled triangle is 30 cm and hypotenuse is 13 cm. Find the length of other two sides.

Question 791763: Perimeter of right angled triangle is 30 cm and hypotenuse is 13 cm. Find the length of other two sides.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
This happens to be one of the basic right triangles that I remember, 5:12:13, but to calculate it perform the following steps.
Let a = one of the legs of the right triangle
Let b = the other leg
Then we have
(1) a + b = 30 - 13 or
(2) a + b = 17 or
(3) a = 17 - b
Now using pythagoreon theorem we have
(4) or
(5)
Now substitute a of (3) into (5) to get
(6) or
(7) or
(8) or using x = b
(9)
Use the quadratic equation to solve for x
(10)
(11) b = 5,12
Let's check this with (1) and (4).
Is (5+12+13 = 30)?
Is (30 = 30)? Yes
Is ()?
Is (169 = 25 + 144)?
Is (169 = 169)? Yes
Answer: the other two sides (legs) are 5cm and 12cm.

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