Question

Does anyone know the answer?

Answer 1

We conclude that the area of the right triangle is:

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

Hence, option A is correct.

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

`=(1)/(2)\left(p+1\right)\left(2p-6\right)`

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

`=(\left(p+1\right)* \: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.