Question

ABC is an isosceles triangle right angled at C with AC = 4 cm. Find the length of AB.

Answer 1

Given:

Triangle ABC is isosceles and right-angled at C.

AC = 4 cm (so AC = BC because the two legs are equal).

Step-wise calculation:

1. Since AC = BC = 4 cm, apply Pythagoras theorem to right triangle ABC:

AB² = AC² + BC²

2. AB² = 4² + 4²

= 16 + 16

= 32

3. `AB = sqrt(32)`

= `sqrt(16 xx 2)` 

= `4sqrt(2) ≈ 5.657` cm   ...(Equivalently, in a 45° – 45° – 90° triangle the hypotenuse = leg × `sqrt(2)`).

AB = 4√2 cm (approximately 5.657 cm).