Question

In∆ABC, LA=x, Lb=3x, and Lc=y, if 3y -5x=30, show that triangle is right angled? ​

Answer 1

Given :

• In ∆ABC, ∠A = x, ∠B = 3x, and ∠C = y, if 3y - 5x = 30,

To find :

• show that triangle is right angled?

Solution :

in a ΔABC

∠A = x°, ∠B= 3x° and ∠C= y°

But ∠A + ∠B + ∠C = 180°

(Sum of angles of a triangle)

x+ 3x +y= 180°

4x + y = 180 . .............. (I)

and 3y - 5x = 30 ........(II)

from (i) y = 180 - 4x

Substituting the value of y in (ii)

3 (180 - 4x) - 5x = 30

540 - 12x - 5x = 30

-17x = -540 +30 = -510

17x = 510 = x = 510/17 = 30

y = 180 - 4x = 180 - 4 x 30

= 180 - 120 - 60

∠A = X = 30°

∠B = 3x = 3 x 30°= 90°

∠C= y = 60°

∠B of ΔABC = 90°

= ΔABC is a right angled triangle.