Question

the area of two similar triangles is 121 cm and 225cm find the ratio of their corresponding medians

Answer 1

Answer:

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Answer 2

Answer:

11:15

Step-by-step explanation:

Concept= Congruency and Area Theorem

Given= 2 similar triangles and their area

To find= Ratio of medians

Explanation=

We have 2 similar triangles . Let them be ΔABC and ΔPQR.

We draw medians in these triangle namely AD(on BC) and PE(on QR). A median divides the side and triangle into half.

Since Triangles are similar, we already know that by congruency ΔABC≈ΔPQR.

so, AB/PQ = BC/QR = AC/PR and ∠B=∠Q;

AB/PQ=(BC/2)/(QR/2) =>  AB/PQ= BD/QE.

Now by SAS, ΔABD and ΔPQE are similar(Congruent)

AB/PQ=AD/PE

∴ ar(ΔABC)/ar(ΔPQR) = AB^2/PQ^2= AD^2/PE^2

=> 121/225 = AD^2/PE^2

=> 11/15 = AD/PE.

Ratio of corresponding median is 11:15.

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