Bob's carpet cleaning company uses the equation y=22x+30 to calculate cost, y, to clean x numbers of rooms. Andy's carpet cleani
ng company uses the table below to calculate the cost to clean rooms.
Laura needs 5 rooms cleaned. Which company charges less and by how much less?
Laura needs 5 rooms cleaned. Which company charges less and by how much less?
1 answer:
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Answer:
The area of △MNP is one fourth of the area of △ABC.
Step-by-step explanation:
It is given that the points M, N, and P are the midpoints of sides AC, BC and AB respectively. It means AC, BC and AB are median of the triangle ABC.
Median divides the area of a triangle in two equal parts.
Since the points M, N, and P are the midpoints of sides AC, BC and AB respectively, therefore MN, NP and MP are midsegments of the triangle.
Midsegments are the line segment which are connecting the midpoints of tro sides and parallel to third side. According to midpoint theorem the length of midsegment is half of length of third side.
Since MN, NP and MP are midsegments of the triangle, therefore the length of these sides are half of AB, AC and BC respectively. In triangle ABC and MNP corresponding side are proportional.
By the property of similar triangles,
Hence proved.
