Question

In which angled ∆ all altitude length are different ?​

Answer 1

Answer:

The following points tell you about the length and location of the altitudes of the different types of triangles: Scalene: None of the altitudes has the same length. Isosceles: Two altitudes have the same length. Equilateral: All three altitudes have the same length.

Answer 2

Step-by-step explanation:

8,15,17

Let the hypotenuse of the triangle be xcm

Let the base of the triangle be ycm

Let the altitude of the triangle be zcm

According to the given equation

x=y+2 and x=2z+1

y=x−2 and z=

2

x−1

Applying Pythagoras theorem

(AC)

2

=(AB)

2

+(BC)

2

x

2

=y

2

+z

2

⇒x

2

=(x−2)

2

+(

2

x−1

)

2

⇒x

2

=

4

4(x−2)

2

+(x−1)

2

⇒4x

2

=4(x

2

+4−4x)+x

2

+1−2x

⇒4x

2

=4x

2

+16−16x+x

2

+1−2x

⇒x

2

−18x+17=0

⇒x

2

−17x−x+17=0

⇒x(x−17)−1(x−17)=0

⇒(x−1)(x−17)=0

x=1 or x=17

If x=1 then y=1−2=−1 that is not possible

So x=17

y=17−2=15

z=

2

17−1

=8

∴ Length of sides of triangle are 17cm,15cm,8cm