9514 1404 393Answer: a) 5 cm b) 8 cm c) 9 mStep-by-step explanation:It can be worthwhile to work the last attachment (a) first, since these are all variations of the same triangle.The Pythagorean theorem tells you the sum of the squares of the legs is the square of the hypotenuse.Problem 6a: 3² +4² = x² . . . . fill in the given numbers; all measures in cm 9 + 16 = x² . . . . simplify exponents 25 = x² . . . . . . . simplify sum x = √25 = 5 . . . take the square root. x = 5 cm . . . . . . apply units__Note that this triangle is a 3-4-5 right triangle. That is a set of side lengths (ratios) that is useful to remember. In this problem set, you see it again immediately.__Problem 6b:Shortest-to-longest, the side ratios of the given triangle are ... 6 : x : 10For some x', this is ... 3 : x' : 5 . . . . . . . . . . . . . matches a 3-4-5 triangle with x' = 4The scale factor is 6/3 = 10/5 = 2, so we have ... x = 2·x' = 2·4 = 8 x = 8 cm . . . . . with units__Problem 6c:The side ratios are ... x : 12 : 15 which reduces to x' : 4 : 5This matches a 3-4-5 triangle with x' = 3, and a scale factor of 12/4 = 15/5 = 3.Then ... x = 3·x' = 3·3 = 9 x = 9 m . . . . . with units