Question

I’m triangle A, the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer leg. What is the length of the 1) shorter leg? 2) Long leg? 3) Hypotenuse?

Answer 1

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