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Question

In a ABC,A=x°,B=(3x)° and C=y°.
If 3y-5x=30, show that the triangle is right-angled.


Solution

In ∆ ABC, we have:
A+B+C=180°     (Angle sum property of a triangle)
∴ ​x + 3x + y = 180
4x + y = 180               ....(i)
Again, 3y − 5x = 30 (Given)
⇒ −5x + 3y = 30         ....(ii)
On multiplying (i) by 3, we get:
12x + 3y = 540           ....(iii)
On subtracting (ii) from (iii), we get:
17x = (540 − 30) = 510
x = 30
On substituting x = 30 in (i), we get:
4 × 30 + y = 180
⇒ 120 + y = 180
y = (180 − 120) = 60
Thus, we have:
 A=30°B=3×30°=90° And, C=60°
Since in the given triangle, one angle is 90°, it is a right-angled triangle.

Mathematics
RS Aggarwal (2015)
Standard X

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