SOLUTION: The area of a triangle is 20 and its base is 16. Find the base of a similar triangle whose area is 45. Please explain.

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Question 1116888: The area of a triangle is 20 and its base is 16. Find the base of a similar triangle whose area is 45. Please explain.
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) About Me  (Show Source):
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The area of a triangle is given by

So if the area is 20 when the base is 16, then , which is to say

Since the larger (area 45) triangle is similar, all dimensions of the two triangles must be in proportion. The ratio of the base to the height of the small triangle must be the same as the ratio of the base to the height of the large triangle. Since when , the desired ratio is . Hence, regardless of the actual height, the base must be 6.4 times larger, which is to say:

Now we can create a single variable equation to describe the larger triangle:











and finally:



John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The ratio of the similar triangles is 20:45 = 4:9. So the ratio of corresponding lengths in the two triangles is sqrt(4):sqrt(9) = 2:3.

The base in the smaller triangle is 16; the base in the larger triangle must be 16*(3/2) = 24.