In triangle ABC, if the sides are in the ratio 3:4:5, what type of triangle is i
Practice Questions
Q1
In triangle ABC, if the sides are in the ratio 3:4:5, what type of triangle is it?
Acute
Obtuse
Right
Equilateral
Questions & Step-by-Step Solutions
In triangle ABC, if the sides are in the ratio 3:4:5, what type of triangle is it?
Step 1: Identify the sides of the triangle based on the ratio 3:4:5. Let's call the sides a, b, and c, where a = 3x, b = 4x, and c = 5x for some positive number x.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides. This can be written as c^2 = a^2 + b^2.
Step 3: Substitute the values of a, b, and c into the Pythagorean theorem: (5x)^2 = (3x)^2 + (4x)^2.
Step 4: Calculate the squares: 25x^2 = 9x^2 + 16x^2.
Step 5: Simplify the right side: 25x^2 = 25x^2.
Step 6: Since both sides of the equation are equal, this confirms that triangle ABC is a right triangle.
