Question

The lines y1 = 2x - 6, y2 = -3x + 4, y3 = -1/2x + 4 are the sides of a right triangle. Find the perimeter and area of the triangle.

Answer 1

The area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

Perimeter and area of the triangle giving the equation of a line

First we will plot the giving lines, determine the point of intersection and then use the Pythagoras theorem to determine the dimension of the right triangle.

From the given equation of the lines, the points of intersection of the line are (x₁, y₁) = (- 0.4, 5.2), (x₂, y₂) = (-0.8, 4.4) and (x₃, y₃) = (0, 4)

For the base

b² = c² -a²

b = √(-0.8)² + (4 - 4.4)²

b = 2√5 / 5

For the height

h = √((- 0.4) - (- 0.8))² + (5.2 - 4.4)²

height = 2√5 / 5

For the hypotenuse

r = √2 · b

r = 2√10 / 5

Determine the Perimeter and area

Perimeter = s1+s2+s3

Perimeter = 2√5 / 5 + 2√5 / 5 + 2√10 / 5

Perimeter = (2√10 + 4√5) / 5 units

For the area

area = 1/2* base * height

A = 0.5 · (2√5 / 5) · (2√5 / 5)

A = 2/5 square units

Hence the area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units

Learn more on area and perimeter of triangles here: brainly.com/question/21511715

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