In △PQR, X is the mid-point of side PR and Y is the midpoint of side QR. If F is the midpoint of line segment XR and S is the midpoint of line segment
In △PQR, X is the mid-point of side PR and Y is the midpoint of side QR. If F is the midpoint of line segment XR and S is the midpoint of line segment YR, what is the area of the △FRS?
I. The area of triangular region PQX is 32.
II. The length of one of the altitudes of triangle PQR is 8.
Answer: A
Can someone please explain how to get the area of △FRS? I am confused with the explanation given in the guide book.
This is a fairly easy question, and is based on similarity.
If you construct the diagram of the triangle as per the question you will see that:
FS || PQ, midpoint theorem.
Besides, FS = 1/2 XY = 1/4 PQ
Thus,
Angle QPX = Angle SFR Corresponding angles
Angle R = Angle R Common Angle
FS/PQ = 1/4 Shown Above
Thus PQX ~ FRS
For two similar triangles,
Ratio of areas of the two triangles = (Ratio of similar sides )^2
Now, lets look at the statements
1.Area of PQX is 32
Area of FSR is 32/(2^4) = 2
Hence, A or D
2. The length of one of the altitudes of triangle PQR is 8.
This information itself does not provide us with anything. So D is eliminated.
Hence, Option A.
