The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find
the other two side
Answers
Let x be the base of the triangle, then the altitude will be (x−7).
By Pythagoras theorem,
x
2
+(x−7)
2
=(13)
2
2x
2
−14x+49−169=0
2x
2
−14x−120=0
x
2
−7x−60=0
x
2
−12x+5x−60=0
(x−12)(x+5)=0
x=12,x=−5
Since the side of the triangle cannot be negative, so the base of the triangle is 12cm and the altitude of the triangle will be 12−7=5cm.
Answer:
Given data:
base of right triangle =x cm
altitude of right triangle = x-7 cm (opposite side)
hypotenuse of right triangle = 13 cm
Step-by-step explanation:
in right angle triangle,
hypotenuse ^ 2 = base ^ 2 + opposite side ^ 2
13^2=x^2+(x-7)^2
169=x^2+x^2-14x+49
120=2x^2-14x
divide the above equation by 2
60=x^2-7x
x^2-7x-60=0
the factors of 60 are 3*4*5
x-12=0 or x+5=0
x=12 cm
The base =12 cm
The altitude =5 cm