Question

# In a If $3y-5x=30,$ show that the triangle is right-angled.

Solution

## In ∆ ABC, we have: $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180°$     (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:   Since in the given triangle, one angle is 90°, it is a right-angled triangle.MathematicsRS Aggarwal (2015)Standard X

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