As you can see in the figure attached, to solve this exercise you must find the value of the length "L". Therefore, you need to follow the proccedure below:
1. You must apply the Pythagorean Theorem, as below:
a²=b²+c²
a is the hypotenuse of the right triangle (a=L).
b and c are the legs of the right triangle (b=L-18; c=L-1)
2. Then, you have:
L²=(L-18)²+(L-1)²
L²=[L²-2(L)(18)+(18)²]+[L²-2(L)(1)+(1)²]
L²=L²-36L+324]+L²-2L+1²
L²-38L+325=0
3. As you can see, you obtain a quadratic equation. You can solve it by factoring. Then:
(L-25)(L-13)=0
L1=25
L2=13
4. You must choose L1=25, because if you decide to use L2=13, you will obtain a negative value in the base of the triangle and the distances can't be negative. Therefore:
L=25 feet
L-18=25-18=7 feet
L-1=25-1=24 feet
The answer is: 24 feet
