Question

What is the perimeter of this triangle?

(-4,5)
(8,5)
(8,-4)
A. 36 units
В.
39 units
33 units
D
42 units

Answer 1

Perimeter of triangle = 12 + 9 + 15

= 36 units

Therefore, option A is correct.

Explanation:

The given points

• (-4, 5)

• (8, 5)

• (8, -4)

From the table, it is clear the side containing the line segment joining the points (-4, 5) and (8, 5) is a straight horizontal line.

Thus, the length of the horizontal distance from the points (-4, 5) and (8, 5) will be:

8-(-4) = 12 units

From the table, it is clear the side containing the line segment joining the points (8, 5) and (8, -4) is a straight vertical line.

Thus, the length of the vertical distance from the points (8, -4) and (8, 5) will be:

5-(-4) = 9

Now, finding the length of the side containing the segment (8, -4) and (-4, 5) using the formula:

`√(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

`=√(\left(-4-8\right)^2+\left(5-\left(-4\right)\right)^2)`

`=√(\left(-4-8\right)^2+\left(5+4\right)^2)`

`=√(12^2+9^2)`

`=√(144+81)`

`=√(225)`

`=√(15^2)`

`\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a`

`=15`

We know that the Perimeter of a rectangle is the length of all the sides of the triangle. Therefore, combining all the lengths of the line segments

Thus,

Perimeter of triangle = 12 + 9 + 15

= 36 units

Therefore, option A is correct.