Question

in triangle PQR , S is a point on QR such that PS is perpendicular to QR. if the area of triangle PQR is 56 square cm square,PS is 8 cm and the ratio of areas of triangle PQR to the area of triangle PQS is 4:3, then find the length of side QR​

Answer 1

Answer:

A) 3/2

B) 7/4

C) 15/8

D) 16/9

E) 2

Image

Let , and .

Given: (i);

Equate the areas: (area of PQR can be calculated by 1/2*leg*leg and 1/2* perpendicular to hypotenuse*hypotenuse) --> (ii);

Aslo (iii);

So, we have:

(i) ;

(ii) ;

(iii) .

From (iii) --> as from (i) and from (ii) then ( --> --> --> ;

From (i) and from (ii) --> solving for and --> and (as given that ).

Next, perpendicular to the hypotenuse will always divide the triangle into two triangles with the same properties as the original triangle. So, PQS and SQR are similar. In two similar triangles, the ratio of their areas is the square of the ratio of their sides: .

So, -->

Answer: D.

Answer 2

Answer:

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Step-by-step explanation: