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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.

Given perimeter of traingle = 30cm hypotenuse = 13cm let the other two sides are a,b a²+b²=13² a²+b²=169 12²+5²=169 or 5²+12²=169 there fore a and b are 12,5