Question

Triangle ABC iść right ta C. AB = 13cm, AC = 12cm and X się tej position on AB such that CX is perpendicular to AB. Find the length CX asa fraction or correct to 2 decimal places.

Answer 1

To find the length of CX, we can use the Pythagorean theorem. Since triangle ABC is a right triangle at C, we have:

AC^2 + BC^2 = AB^2

Substituting the given values, we get:

12^2 + BC^2 = 13^2

144 + BC^2 = 169

BC^2 = 25

BC = 5

Now, since CX is perpendicular to AB, triangles ACX and BXC are similar. Therefore:

CX/BC = AC/AB

Substituting the given values, we get:

CX/5 = 12/13

Cross-multiplying, we get:

CX = 60/13

Therefore, the length of CX as a fraction is 60/13 or as a decimal rounded to 2 decimal places is approximately 4.62.