Question

Given a right triangle with sides of length a, b, and c and area a²+b²-c², find c/b, the ratio of the legs of the right triangle.

Answer 1

Answer:

4

Step-by-step explanation:

Looking at the sketch we can formulate 2 equations:

Pythag: $b^{2} +c^{2} =a^{2}$

Area of triangle= $\frac{1}{2} bc$

But area also = $a^{2} +b^{2} -c^{2}$ (from the question)

Therefore $\frac{1}{2} bc$ =  $a^{2} +b^{2} -c^{2}$

But we can sub in the expression for $a^{2}$ from pythag. ($b^{2} +c^{2} =a^{2}$)

$\frac{1}{2} bc= b^{2} +c^{2} +b^{2} -c^{2}$

$\frac{1}{2} bc=2b^{2}$

$bc=4b^{2}$

$c=4b$

$c/b= 4b/b=4$