The attitude of a right triangle is 7cm less than its base. If the hypotenuse is 13cm find the other two sides solution in 10 class
Given that,
The altitude of a right triangle is 7 cm less than its base.
So, let's assume that
The base of right-angle triangle is x cm.
So,
Altitude of right-angle triangle is x - 7 cm.
Thus, we have In right angle triangle
Base = x cm
Altitude = x - 7 cm
Hypotenuse = 13 cm
Now, By using Pythagoras Theorem , we have
Base²+Altitude² = Hypotenuse²
So, on substituting the values, we get
x² + (x-7)² = 13²
x² + x² + 49 - 14x = 169
2x² + 49 - 14x = 169
2x² + 49 - 14x - 169 = 0
2x² - 14x - 120 = 0
2(x² - 7x - 60) = 0
x² - 7x - 60 = 0
x(x - 12) + 5(x - 12) = 0
(x - 12)(x + 5) = 0
x = 12 or x = -5 (not possible)
So,
Base of right-angle triangle = 12 cm
Altitude of right angle triangle = 12 - 7 = 5 cm
