In triangle ABC p,q,r such that they lie interior of triang ABC and AP=AR and all the three sides of triangle PQR are scalan if area of triangle PQR is 100 then find area of triangle ABC
Is your school subject the name of your school, or is it geometry?
To find the area of triangle ABC, we need to use the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.
Given that PQR is a scalene triangle with an area of 100, we can use this information to find the area of triangle ABC.
Let's first identify the corresponding side lengths of triangles ABC and PQR. Since AP = AR, triangle PQR is similar to triangle ABC, and the ratio of their corresponding side lengths is:
PQ / AC = QR / BC = PR / AB.
Since all the three sides of triangle PQR are scalene, this means that the ratio of the corresponding side lengths is different for each pair of sides. Let's call these ratios a, b, and c:
PQ / AC = a,
QR / BC = b,
PR / AB = c.
Now, we can use the information about the area of triangle PQR to set up an equation:
(area of triangle PQR) / (area of triangle ABC) = (PQ / AC)^2 = a^2.
Since the given area of triangle PQR is 100, we can write:
100 / (area of triangle ABC) = a^2.
To find the area of triangle ABC, we need to find the value of a.
Unfortunately, the information provided is not sufficient to determine the value of a or the area of triangle ABC. We would need additional information about the relationship between the side lengths of triangles ABC and PQR in order to solve for the area of triangle ABC.