Math Problem Statement

In a right triangle \(ABC\), where \( \angle C \) is right angled, if the ratio of the lengths of \( AC \) and \( BC \) is \( 5:12 \) and the length of the hypotenuse \( AB \) is \( 13 \) cm, then what will be the lengths of \( AC \) and \( BC \)? Also, calculate the area of ​​the triangle and state whether it is more than \( 40 \) sq. cm. Also, if \( D \) is a point on \( AC \) and the length of \( AD \) is \( 7 \) cm, then what will be the length of \( DC\)?

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Triangles
Pythagorean Theorem
Area Calculation

Formulas

Pythagorean Theorem: AB^2 = AC^2 + BC^2
Area of a triangle: Area = (1/2) * base * height

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9