practice problems pending

Q1. Two sides of a triangle are 10 cm and 5 cm in length, and the length of the median to the third side is 6.5 cm. If the area of the triangle is 6.sqrt(p) cm^2 then find the value of 'p.
S1.
By Apollonius theorem, third side is 9.
Now use heron's formula to get answer p = 15 

Q2.

Two sides of a triangle are sqrt(3) units and sqrt(2) units. The medians to these two sides are mutually perpendicular. Prove that the third side has an integer measure.
S2.


(2x)^2 + y^2 = 1/2 = 4x^2 + y^2
(2y)^2 + x^2 = 3/4
5x^2 + 5y^2 = 5/4
4x^2 + 4y^2 = 1 = (2x)^2 + (2y)^2  = BC^2 => BC = 1 H.P.


Q3. ABC is a triangle in which Angle B = 2 (Angle C).
D is a point on BC such that AD bisects Angle BAC and AB = CD.
Prove that Angle BAC = 72 deg.

S3.





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