The altitude of a right triangle is 7cm less than it's base . if the hypotenuse is 13 cm, find the other two sides.
Answers
Given:
The altitude of a right triangle is 7cm less then it's base the hypotenus is 13 cm.
Find:
The other two side.
Solution:
Let the base of the right triangle be x cm.
it's altitude = (x - 7) cm
From Pythagoras theorem;
Base² + Altitude ² = Hypothesis ²
Therefore,
=> x² + (x - 7)² = 13²
=> x² + x² + 49 - 14x = 169
=> 2x² - 14x - 169 - 49 = 0
=> 2x² - 14x - 120 = 0
=> 2(x² - 7x - 60) = 0
=> x² - 7x - 60 = 0
=> x² - 12x + 5x - 60 = 0
=> x(x - 12) + 5(x - 12) = 0
=> (x - 12) (x + 5) = 0
=> x - 12 = 0 or x + 5 = 0
=> x = 12 0r x = -5
Since,
sides are positive x can only be 12.
Therefore,
The base of the triangle is 12cm and altitude of the triangle be (12 - 7)cm = 5cm.
Hence, the others two sides is 12cm and 5cm.
I hope it will help you.
Regards.
Answer:
=> x² + (x - 7)² = 13²
=> x² + x² + 49 - 14x = 169
=> 2x² - 14x - 169 - 49 = 0
=> 2x² - 14x - 120 = 0
=> 2(x² - 7x - 60) = 0
=> x² - 7x - 60 = 0
=> x² - 12x + 5x - 60 = 0
=> x(x - 12) + 5(x - 12) = 0
=> (x - 12) (x + 5) = 0
=> x - 12 = 0 or x + 5 = 0
=> x = 12 0r x = -5
Step-by-step explanation: