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love history [14]
1 year ago
8

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

of the triangle.
Mathematics
1 answer:
tino4ka555 [31]1 year ago
3 0

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

<h3>Determining the perimeter and area of the triangle giving line equation</h3>

In order to determine the area and perimeter of the lines, 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.

The points of intersection of the line are;

(x₁, y₁) = (- 0.4, 5.2),

(x₂, y₂) = (-0.8, 4.4),

(x₃, y₃) = (0, 4)

Determine the base

b² = c² -a²

b = √(-0.8)² + (4 - 4.4)²

b = 2√5 / 5

Determine 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

<h3>Determine the Perimeter and area</h3>

Perimeter = s1+s2+s3

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

Perimeter = (2√10 + 4√5) / 5 units

<u>For the area</u>

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/12010318

#SPJ1

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