Question

Does anyone know the answer?

Answer 1

Answer:

We conclude that the area of the right triangle is:

$A\:=p^2-2p-3$

Hence, option A is correct.          

Step-by-step explanation:

From the given right-angled triangle,

• Base = p+1

• Perpendicular = 2p-6

Using the formula to determine the area of the right-angled triangle

Area of the right triangle A = 1/2 × Base × Perpendicular

                                            $=\frac{1}{2}\left(p+1\right)\left(2p-6\right)$

Factor 2p-6: 2(p-3)

                                             $=\frac{\left(p+1\right)\times \:2\left(p-3\right)}{2}$  

Divide the number: 2/2 = 1

                                              $=\left(p+1\right)\left(p-3\right)$

$\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

                                               $=pp+p\left(-3\right)+1\cdot \:p+1\cdot \left(-3\right)$

                                               $=pp-3p+1\cdot \:p-1\cdot \:3$

                                                $=p^2-2p-3$

Therefore, we conclude that the area of the right triangle is:

$A\:=p^2-2p-3$

Hence, option A is correct.