We have this equation. A²+B²=C² We have bits of information that'll help us simplify the equation so there's only one variable. The longer leg, A, is 3 inches more than the length of the shorter leg, B, tripled. A=3B+3 Let's plug that in. (3b+3)²+B²=C² The hypotenuse, C, is 3 inches less than four times the length of the shorter leg. C=4B-3 Let's plug that in. (3b+3)²+B²=(4B-3)² Let's solve. 9B²+18B+9+B²=16B²-24B+9 10B²+18B+9=16b²-24b+9 Let's subtract 9 from both sides. 10b²+18b=16b²-24b Let's subtract 10b² from both sides. 18b=6b²-24b Let's add 24b from both sides. 42b=6b² Let's divide each side by 6. 7b=b² With this, you can tell that b is 7 since it times 7 equal itself squared. The shorter leg is 7 inches. Now, let's look back at the bits of information. The longer leg of a right triangle is 3 inches more than the length of the shorter side tripled. 3(7)+3=24 So, the longer side is 24. We can either use the other information or plug it into the equation. We can do both. The hypotenuse is 3 less than four times the shorter leg. 4(7)-3=25 7²+24²= 49+576=625 √625=25 So, the length of the hypotenuse is 25 inches.
