If the ratio of the sides of a triangle is 3:4:5, what type of triangle is it? (2019)
Practice Questions
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Q1
If the ratio of the sides of a triangle is 3:4:5, what type of triangle is it? (2019)
Equilateral
Isosceles
Scalene
Right-angled
A triangle with sides in the ratio 3:4:5 is a right-angled triangle.
Questions & Step-by-step Solutions
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Q
Q: If the ratio of the sides of a triangle is 3:4:5, what type of triangle is it? (2019)
Solution: A triangle with sides in the ratio 3:4:5 is a right-angled triangle.
Steps: 7
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.
