The areas of two similar triangles are 100 cm2 and 64 cm2, respectively. If the median of the bigger triangle is 5 cm, then the corresponding median of the smaller triangle is:
Question
The areas of two similar triangles are 100 cm2 and 64 cm2, respectively. If the median of the bigger triangle is 5 cm, then the corresponding median of the smaller triangle is:
Solution
The areas of similar figures are proportional to the square of the ratio of their corresponding lengths. This includes medians.
Step 1: Find the ratio of the areas of the two triangles. This is 100 cm² / 64 cm² = 1.5625.
Step 2: To find the ratio of the corresponding lengths (including medians), take the square root of the ratio of the areas. The square root of 1.5625 is 1.25.
Step 3: If the median of the larger triangle is 5 cm, then the median of the smaller triangle is 5 cm / 1.25 = 4 cm.
So, the corresponding median of the smaller triangle is 4 cm.
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