One leg

One leg of a right triangle is 1 foot longer than the other leg. The hypotenuse is 5 feet. Find the lengths of the three sides of the triangle.

Correct answer:

c =  5 ft
a =  4 ft
b =  3 ft

Step-by-step explanation:

$c=5=5\text{ft}$

$$\begin{gathered} a=1+b \\ {a}^2+b^2=c^2 \\ {a}^2+(a-1{)}^2=c^2 \\ {a}^2+(a-1{)}^2=5^2 \\ 2a^2-2a-24=0 \\ 2...\text{ prime number} \\ 24=2^3\cdot 3 \\ \text{GCD}(2,2,24)=2 \\ {a}^2-a-12=0 \\ p=1;q=-1;r=-12 \\ D=q^2-4pr=1^2-4\cdot 1\cdot (-12)=49 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{1\pm \sqrt{49}}{2} \\ {a}_{1,2}=\frac{1\pm 7}{2} \\ {a}_{1,2}=0.5\pm 3.5 \\ {a}_1=4 \\ {a}_2=-3 \\ a=a_1=4=4\text{ft} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=a-1=4-1=3\text{ft}$

Try another example