Question

The verticles of triangle ABC are: A(-2, -2), B(-5,-4),C(4,1). Round your answer to the nearest tenth.

a. Find the perimeter of the triangle

B. Find the area of the triangle

C. Johnathon says the triangle is a right triangle.
Do you agree or disagree. Why or why not ?

Answer 1

The verticles of triangle ABC are: A(-2, -2), B(-5,-4), C(4,1). Round your answer to the nearest tenth.

1. Find the perimeter of the triangle

2. Find the area of the triangle

3. Johnathon says the triangle is a right triangle. Do you agree or disagree. Why or why not?

Solution:

1. Perimeter of the triangle

$AB=\sqrt{(-5+2)^{2}+(-4+2)^{2}}=\sqrt{13}$

$BC=\sqrt{(-5-4)^{2}+(-4-1)^{2}}=\sqrt{106}$

$AC=\sqrt{(4+2)^{2}+(1+2)^{2}}=\sqrt{45}$

$P=AB+BC+AC\approx 20.6$

2. Area of the triangle

Solution using Heron’s formula

$p=\frac{P}{2}$

$S=\sqrt{p(p-AB)(p-AC)(p-BC)}\approx 1.5$

Solution using cross product

$AB=(-3,-2)$

$AC=(6,3)$

$S=\frac{1}{2}|AB\times AC|=\frac{3}{2}=1.5$

3. Disagree. Right triangle must satisfy Pythagorean theorem.

$AC^{2}+AB^{2}=13+45=58$

$BC^{2}=106$

$AC^{2}+AB^{2}\neq BC^{2}$

Answer:

1. $20.6$

2. $1.5$

3. Disagree. Right triangle must satisfy Pythagorean theorem.