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,
Base^2 + Altitude^2 = Hypotenuse^2
∴ x^2 + (x – 7)^2 = 132
⇒ x^2 + x^2 + 49 – 14x = 169
⇒ 2x^2 – 14x – 120 = 0
⇒ x^2 – 7x – 60 = 0
⇒ x^2 – 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:
Let, the base of the triangle ⛛ = y says
The altitude of the triangle ⛛ is 7cm less than its base = y-7
Given,
Hypotenuse = 13cm
By P.T
(Hypotenuse)^2=(altitude)^2+(base)^2
➡️13^2=(y-7)^2+y^2
➡️169=y^2+49-14y+y^2
➡️169=2y^2-14y+49
➡️2y^2-14y+49-169=0
➡️2y^2-14y-120=0
➡️y^2-7y-60=0
➡️y^2+5y-12y-60=0
➡️y(y+5)-12(y+5)=0
➡️(y-12)(y+5)=0
➡️y=12 (or) y=-5
➡️So, y= 12
Because 'y' value cannot be negative (-ve)
Therefore, the base of the triangle ⛛ = y=12cm
Then the altitude of the triangle ⛛ =y-7=12-7=>5cm
FOLLOW AND THANK MY ANSWERS [tex]