Question

4. ∆ABC ~ PQR. If AB : PQ=4:5,
find A(∆ABC): A(∆PQR).​

Answer 1

Answer:

4:5

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Answer 2

Given:

AB: PQ=4:5,

∆ABC ~ ∆PQR

To find:

Δ(∆ABC): Δ(∆PQR)

Solution:

The required value of Δ(∆ABC): Δ(∆PQR) is 16: 25.

We can find the required ratio by taking the square of the sides' ratio that are corresponding to each other.

In the triangles ABC and PQR, the sides that are corresponding are as follows-

AB/PQ=BC/QR=AC/PR

The square of these ratios is equal to the ratio of the given triangles' areas.

Using the values, we get

Δ(∆ABC): Δ(∆PQR)=$AB^{2} :PQ^{2}$

Δ(∆ABC): Δ(∆PQR)=$4^{2} :5^{2}$

Δ(∆ABC): Δ(∆PQR)=16: 25

Therefore, the required value of Δ(∆ABC): Δ(∆PQR) is 16: 25.