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The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
In a right triangle, altitude is one of the sides.
Let the base be x cm.
The altitude will be (x - 7) cm.
We can now apply the Pythagoras theorem to the given right triangle.
Pythagoras theorem: Hypotenuse2 = (side 1)2 + (side 2)2
132 = x2 + (x - 7)2
132 = x2 + (x - 7)2
169 = x2 + x2 - 14x + 49
169 = 2x2 - 14x + 49
2x2 - 14x + 49 -169 = 0
2x2 - 14x - 120 = 0
(2x2 - 14x - 120) / 2 = 0
x2 - 7x - 60 = 0
x2 - 12x + 5x - 60 = 0
x(x - 12) + 5 (x - 12) = 0
(x + 5) (x - 12) = 0
x - 12 = 0 and x + 5 = 0
x = 12 and x = - 5
We know that the value of the base cannot be negative.
Therefore, Base = 12 cm, Altitude = 12 - 7 = 5 cm
☛ Check: NCERT Solutions for Class 10 Maths Chapter 4
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides
Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.2 Question 5
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm then the other two sides are 12 cm and 5 cm.
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