Answer:
a=2.69 in
b=11.37 in
c=11.69 in
Explanation:
If we mark shorter side as a, we can write all sides expressed through a.
So:
- short side is a
- longer side is 6 in longer then twice the length of short side b = 2a + 6
- hypotenuse is 9 in longer then short leg c = a + 9
Now we can write the Pythagoras theorem a^2 + b^2 = c^2 as:
a^2 + (2a + 6)^2 = (a + 9)^2
a^2 +4a^2+24a+36 = a^2+18a+81
When we solve this, we get:
4a^2 + 6a - 45 = 0
Now we have a quadratic equation which can be solved as:
x = -b ± √(b^2 - 4ac) / 2a
When we plug in the values, we get that x equals 2.69 or -4.19
It's obvious that length of a side can not be negative, which means that a = 2.69 in.
Side b is 2a + 6, which is 11.37 and c is a + 9 which is 11.69 inches.
These are lengths rounded to two decimals so due to this approximation they may not be completely precise.
