The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. What type of triangle is it?
Practice Questions
1 question
Q1
The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. What type of triangle is it?
Acute
Obtuse
Right
Equilateral
Since 7^2 + 24^2 = 25^2, triangle ABC is a right triangle.
Questions & Step-by-step Solutions
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Q
Q: The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. What type of triangle is it?
Solution: Since 7^2 + 24^2 = 25^2, triangle ABC is a right triangle.
Steps: 7
Step 1: Identify the lengths of the sides of triangle ABC. They are 7 cm, 24 cm, and 25 cm.
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.
Step 3: Identify the longest side. Here, the longest side is 25 cm.
Step 4: Calculate the square of each side: 7^2 = 49, 24^2 = 576, and 25^2 = 625.
Step 5: Add the squares of the two shorter sides: 49 + 576 = 625.
Step 6: Compare the sum with the square of the longest side: 625 (from the sum) equals 625 (from 25^2).
Step 7: Since the equation 7^2 + 24^2 = 25^2 holds true, triangle ABC is a right triangle.
