Q2 of 53 Page 156

In ΔABC m∠A = m∠B + m∠C, AB = 7, BC = 25. Find the perimeter of ΔABC.

Let m∠A = x


Sum of interior angles = mA = mB + mC


⇒ mA + mB + mC = 180 (Sum of interior angle of triangle is 180)


⇒ 2x = 180


⇒ x = 90


So ∠A is right angled


Applying Pythagoras theorem


AC2 = BC2 – AB2


⇒ AC2 = 252 – 72


⇒ AC2 = 576


⇒ AC = 24


Perimeter of ΔABC = (25 + 24 + 7) = 56 units.


More from this chapter

All 53 →
14

AB = AC and ∠A is right angle in ΔABC. If BC = √2 a, then find the area of the triangle. (a ∈ R, a > 0)

 1

In rectangle ABCD, AB + BC = 23, AC + BD = 34. Find the area of the rectangle.

 3

A staircase of length 6.5 meters touches a wall at height of 6 meter. Find the distance of base of the staircase from the wall.

 4

In ΔABC AB = 7, AC = 5, AD = 5. Find , if the mid – point of BC is D.