EXPLANATION
We need to apply the Pythagorean Theorem in order to get the left unkwnown side:
[tex]Hypotenuse^2=Smaller\text{ leg}^2+Larger\text{ leg}^2[/tex]
Plugging in the terms into the expression:
[tex]14^2=9^2+larger\text{ leg\textasciicircum2}[/tex]
Computing the powers:
[tex]196=81+larger\text{ leg}^2[/tex]
Subtracting -81 to both sides:
196 - 81 = larger leg^2
Applying the square root to both sides:
[tex]\sqrt{115}=larger\text{ leg}[/tex]
Computing the root:
[tex]larger\text{ leg=10.723}[/tex]
Now, with the obtained larger leg, we can compute the area, with the following equation:
[tex]Area_{triangle}=\frac{base*height}{2}=\frac{9*10.723}{2}[/tex]
Multiplying numbers:
[tex]Area_{triangle}=48.2in^2[/tex]
Now, we need to compute the perimeter by adding all the legs, as shown as follows:
[tex]Perimeter=9in+14in+10.72in=33.72in[/tex]
The solutions are the following:
Area= 48.2 in^2
Perimeter= 33.7 in
