Question

pls answer this question ​

Answer 1

Step-by-step explanation:

1) To prove both the triangles similar , we need to just prove that each of the corresponding angles of triangle are equal.

So, now in triangle PQR and triangle SPR

angle PSR = angle QPR (given in the question)

angle PRS = angle PRQ ( same angle)

Now , if any two angles of triangle are equal the third angle will be automatically equal.

so, angle SPR = angle PQR.

NOW we can say that both triangle are similar

PQR ~ SPR.

2) Now , as we know that both traingles are similar then their each sides will be in proportion to each other we need to find that proportion first. So, for that take any know two respective sides from both the triangles.

PR and SR

PR = 6cm

SR = 3cm.

so ratio between these two sides will be 2:1.

So now each respective sides ratio will be 2:1 only.

So, length of PS will be in ratio with QP as they are the respective sides of yhe triangle and if QP is 8cms then with 2:1 ratio PS will be 4cm

length of PS = 4cms.

Now QR and PR are the respective sides . So, with 2:1 ratio if PR is 6cm then QR will be 12cms.

length of QR = 12cms.

3) Now for finding the ratio of area of both the trianlges , we need to find the ratio of any corresponding side of the triangles and then square it.

Now, we already have the ratio of corresponding sides which is 2:1

now square of this ratio will be 4:1

So, area of PQR : area of SPR = 4 : 1

HOPE THIS WILL HELP YOU.

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