Question

ABC is an isosceles triangle right angled at "c"and AB2=n.ac2then n=​

Answer 1

Answer:

hi guys

Step-by-step explanation:

In ΔABC, ∠ACB = 90° and AC = BC [Since, ABC is an isosceles triangle right angled at C]

Using Pythagoras theorem,

⇒ AB2 = AC2 + BC2

⇒ AB2 = AC2 + AC2  [Since  AC = BC]

Therefore, AB2 = 2 AC2

Answer 2

Concept

This question requires knowledge of the Pythagoras theorem.

Pythagora's theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Given:

Triangle ABC is an isosceles right-angled triangle at C

$AB^2=nAC^2$

To find:

The value of n

Solution:

Since it is an isosceles triangle

We know,

AC=BC

Applying Pythagoras theorem to triangle ABC we get,

$A B^{2}=A C^{2}+B C^{2}$

$\Rightarrow A B^{2}=A C^{2}+A C^{2}$

[ Since BC=AC ]

⇒$AB^2=2AC^2$ ----------------------(1)

It is also given in the question that

$AB^2=nAC^2$     ----------------------(2)

Comparing equations (1) and (2) we get.

$2AC^2=nAC^2$

Therefore,

n=2