Question

The areas of two similar triangles are 81 cm sq . and. 49 cm sq . Find the ratio of their corresponding median.
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Answer 1

Answer:

Step-by-step explanation:

SOLUTION :  

Given : Area of two similar triangles is 81cm² and 49cm² .

(i) Since, the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding altitudes.

ar(∆1)/ar(∆2) = (altitude 1/ altitude 2)²

81/49 = (altitude 1/ altitude 2)²

On taking square root on both sides,

√81/49 = √(altitude 1/ altitude 2)²

9/7 = altitude 1/ altitude 2

Altitude 1: altitude 2 = 9 : 7

Hence, the ratio of their corresponding Heights (altitudes) is 9 : 7.

 

(ii) Since, the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding medians.

ar(∆1)/ar(∆2) = (median1/median2)²

81/49 = (median1/median2)²

On taking square root on both sides,

9/7 = median 1/median2

Median 1: median 2 = 9: 7

Hence, the ratio of their corresponding medians is 9 : 7.

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Answer 2

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