The areas of two similar triangles are 81cm square and 49 cm square respectively .Find the ratio. of their corresponding heights.what is the ratio of their corresponding medians??
Answers
Answer:
Step-by-step explanation:
if there are two similar triangles and their areas are A1 and A2 and heights h1 and h2 respectively.
then
(h1/h2)²= A1/A2
(h1/h2)²=81/49
h1/h2=9/7
THEREFORE THE RATIO OF THE CORRESPONDING HEIGHTS
9:7
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Answer:
9:7
Step-by-step explanation:
Assume two similar triangles having area 81 cm² and 49 cm² respectively.
We have to find the ratio of their corresponding heights and the ratio of their corresponding medians.
As said in question they are similar triangles. So, the ratio of area of two traingles = Ratio of square of height = Ratio of square of their medians.
By area of similar triangle theorem,
(Area of first triangle)/(Area of second triangle) = (Side of first triangle)²/(Side of second triangle)²
(Side of first triangle)/(Side of second triangle) = √81/49
(Side of first triangle)/(Side of second triangle) = 9/7
As, the ratio of the area of two similar triangles is equal to the ratio of the squares of their corresponding altitudes and it is also equal to the squares of their corresponding medians.
Hence, the ratio of altitudes and the tatio of medians is 9:7.