So the formula to find the hypotenuse is: A²+B²=C² We can use the bits of information to help us. The longer leg, A, is 6 more than the shorter leg, B. This means A=B+6 Let's plug this in. (b+6)²+b²=C² The hypotenuse is 6 more than the longer leg. Since we're trying to limit it to one variable, we know that the hypotenuse is 12 longer than the short leg since the long leg is 6 longer than the short leg. (B+6)²+B²= (B+12)² Let's multiply. b²+12b+36+b²=b²+24B+144 2b²+12b+36=B²+24B+144 Let's subtract 12b from both sides. 2B²+36= B²+12B+144 Let's subtract B² from both sides. B²+36=12B+144 Let's subtract 36 from both sides. B²=12B+108 Let's subtract 12b from both sides. B²-12B=108 B=18 The shorter leg is 18 units. The longer leg is 6 more, so 24 units. The hypotenuse is 6 more than the longer leg, so 30. Shorter leg=18 units Longer leg= 24 units Hypotenuse=30 units
