Answer:
We conclude that the area of the right triangle is:
[tex]A\:=p^2-2p-3[/tex]
Hence, option A is correct.
Step-by-step explanation:
From the given right-angled triangle,
Using the formula to determine the area of the right-angled triangle
Area of the right triangle A = 1/2 × Base × Perpendicular
[tex]=\frac{1}{2}\left(p+1\right)\left(2p-6\right)[/tex]
Factor 2p-6: 2(p-3)
[tex]=\frac{\left(p+1\right)\times \:2\left(p-3\right)}{2}[/tex]
Divide the number: 2/2 = 1
[tex]=\left(p+1\right)\left(p-3\right)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
[tex]=pp+p\left(-3\right)+1\cdot \:p+1\cdot \left(-3\right)[/tex]
[tex]=pp-3p+1\cdot \:p-1\cdot \:3[/tex]
[tex]=p^2-2p-3[/tex]
Therefore, we conclude that the area of the right triangle is:
[tex]A\:=p^2-2p-3[/tex]
Hence, option A is correct.
