Let ABC be a right-angled triangle such that ∠C = 90°. Let D be a point on AB such that CD is perpendicular to AB. If AC = 5 cm and BC = 12 cm, find the length of CD (in cm).

Correct option is A

Given:

AC = 5 cm and BC = 12 cm
Formula Used:
Pythagoras’ theorem
Area of triangle = $$\frac{1}{2} b\times h$$​​
Solution:
​$$(AB)^2 = (AC)^2 + (BC)^2 \\\ \\(AB)^2 = (5)^2 + (12)^2\\\ \\(AB) = √(25+144)$$​​
AB=13cm
Area of triangle is same
​$$\frac{1}{2}(AC) \times(BC) = \frac{1}{2} \times(AB)\times(CD) \\\ \\5\times 12 = 13 \times CD\\\ \\CD =\frac{60}{13} cm$$​​