If ∆ABC ~ ∆QRP, ar(∆ABC) 9 AB = 18 cm andar(∆PQR) 4BC = 15 cm, then find the length of PR.
Question
If ∆ABC ~ ∆QRP, ar(∆ABC) 9 AB = 18 cm andar(∆PQR) 4BC = 15 cm, then find the length of PR.
Solution
The given question states that ∆ABC ~ ∆QRP. This means that the triangles are similar and their corresponding sides are in proportion.
The area of similar triangles is proportional to the square of the ratio of their corresponding sides.
So, we can write the ratio of the areas of ∆ABC and ∆QRP as:
ar(∆ABC) / ar(∆QRP) = (AB/PR)²
Given that ar(∆ABC) = 9 and AB = 18 cm, and ar(∆QRP) = 4 and BC = 15 cm, we can substitute these values into the equation:
9 / 4 = (18 / PR)²
Solving for PR, we get:
PR = 18 / √(9/4) = 18 / (3/2) = 12 cm
So, the length of PR is 12 cm.
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