ABC is an isosceles triangle in which angle C = 90 degrees . If AC = 6cm , then find the AB?

Question

Answer

Angle C = 90 degree

Isosceles triangle have two equal sides

So, AC = AB

Hence , AC = 6 cm

Answer

Answer

Understanding the Triangle
In triangle ABC, we have the following characteristics:
- Angle C = 90 degrees, indicating that triangle ABC is a right-angled triangle.
- AC = 6 cm, one of the legs of the triangle.
- Since ABC is isosceles, the two legs (AC and BC) must be equal in length.
Finding the Length of AB
To find the length of AB, which is the hypotenuse of the right-angled triangle, we can use the Pythagorean theorem. The theorem states:
- For any right-angled triangle: a^2 + b^2 = c^2, where:
- a and b are the legs, and
- c is the hypotenuse.
Applying the Pythagorean Theorem
Given that:
- AC = 6 cm (this is one leg),
- BC = AC = 6 cm (because the triangle is isosceles),
We substitute the values into the theorem:
- (6 cm)^2 + (6 cm)^2 = AB^2
- 36 + 36 = AB^2
- 72 = AB^2
Now, to find AB:
- AB = √72 cm
- AB = √(36 * 2) = 6√2 cm
Conclusion
Thus, the length of side AB in the isosceles right triangle ABC is:
- AB = 6√2 cm, approximately equal to 8.49 cm.
This solution illustrates the relationship between the sides in an isosceles right triangle and effectively employs the Pythagorean theorem for finding the hypotenuse.

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