If the ratio of the sides of a triangle is 3:4:5, what type of triangle is it? (

If the ratio of the sides of a triangle is 3:4:5, what type of triangle is it? (2019)

If the ratio of the sides of a triangle is 3:4:5, what type of triangle is it? (2019)

Step 1: Understand that the sides of the triangle are in the ratio 3:4:5.
Step 2: Recognize that these numbers (3, 4, and 5) can represent the lengths of the sides of a triangle.
Step 3: Recall the Pythagorean theorem, which states that in a right-angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 4: Identify the longest side in the ratio 3:4:5, which is 5.
Step 5: Calculate the squares of the sides: 3^2 = 9, 4^2 = 16, and 5^2 = 25.
Step 6: Check if the Pythagorean theorem holds: 9 + 16 = 25.
Step 7: Since 9 + 16 equals 25, the triangle with sides in the ratio 3:4:5 is a right-angled triangle.

Triangle Ratios – Understanding the significance of side ratios in determining the type of triangle.
Pythagorean Theorem – Recognizing that a triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, indicating it is a right triangle.