The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Answers
Let us say, the base of the right triangle be x cm.
Given,
the altitude of right triangle = (x – 7) cm
From Pythagoras theorem,
we know,
Base² + Altitude² = Hypotenuse²
∴ x² + (x – 7)² = 13²
➪ x² + x² + 49 – 14x = 169
➪ 2x² – 14x – 120 = 0
➪ x² – 7x – 60 = 0
➪ x² – 12x + 5x – 60 = 0
➪ x(x – 12) + 5(x – 12) = 0
➪ (x – 12)(x + 5) = 0
Thus, either x – 12 = 0 or x + 5 = 0,
➪ x = 12 or x = – 5
Since sides cannot be negative, x can only be 12.
Therefore, the base of the given triangle is 12 cm and the altitude of this triangle will be (12 – 7) cm = 5 cm.
Answer:
∴ x² + (x – 7)² = 13²
➪ x² + x² + 49 – 14x = 169
➪ 2x² – 14x – 120 = 0
➪ x² – 7x – 60 = 0
➪ x² – 12x + 5x – 60 = 0
➪ x(x – 12) + 5(x – 12) = 0
➪ (x – 12)(x + 5) = 0
Thus, either x – 12 = 0 or x + 5 = 0,
➪ x = 12 or x = – 5
Since sides cannot be negative, x can only be 12.
Therefore, the base of the given triangle is 12 cm and the altitude of this triangle will be (12 – 7) cm = 5 cm.