Answer:
The shorter leg of the right triangle is [tex]5\ cm[/tex]
The other leg of the right triangle is [tex]12\ cm[/tex]
Step-by-step explanation:
Let
x-----> the shorter leg of a right triangle
y----> the larger leg of a right triangle
we know that
Applying the Pythagoras Theorem
[tex]13^{2}=x^{2} +y^{2}[/tex] ----> equation A
[tex]x=y-7[/tex] ----> equation B
substitute equation B in equation A and solve for y
[tex]13^{2}=(y-7)^{2} +y^{2}\\169=y^{2} -14y+49+y^{2} \\2y^{2}-14y-120=0[/tex]
using a graphing tool----> solve the quadratic equation
The solution is [tex]y=12\ cm[/tex]
see the attached figure
Find the value of x
[tex]x=12-7=5\ cm[/tex]
therefore
The shorter leg of the right triangle is [tex]5\ cm[/tex]
The other leg of the right triangle is [tex]12\ cm[/tex]
