26. In △PQR, PM is a median. Is it true to say that PQ + QR + RP > 2 PM. Prove it.
27. One of the base angles in an isosceles triangle is 33°. Find the remaining two angles.
28. A ladder 13 m long is leaning against a wall. The foot of the ladder is 12 m away from
the wall. Find the height up to which the ladder reaches the wall.
29. The angles of a △ABC are (2x – 5)°, (x – 3)° and x°. Find the value of x and hence
measure of all the angles of △ABC.
30. In △ ABC find the value of x if ∠BAE = 125° and
∠ACF = 116°
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Answer:
Answer 26.
Theorem: In a triangle , sum of the length of any two sides is greater than the third side.
Draw the triangle and join the points P and S
In the figure,
In ΔPQS, according to the theorem,
PQ+QS>PS ........... (1)
In ΔPSR, according to the theorem,
PR+SR>PS ........... (2)
Adding (1) and (2),
PQ+QS+SR+PR>PS+PS
PQ+(QS+SR)+PR>2PS
PQ+QR+PR>2PS
solution
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