Digital SATMath: Geometry and TrigonometryMedium
A gardener is planting flowers in a triangular bed. The bed has sides of length 7 feet, 8 feet, and 13 feet. What type of triangle is formed by the flower bed?
- AEquilateral triangle
- BAcute triangle
- CRight triangle
- DObtuse triangle
Show answer & explanationAnswer & explanation
Correct answer: D. Obtuse triangle
To determine the type of triangle based on its angles, compare the square of the longest side (c^2) to the sum of the squares of the other two sides (a^2 + b^2). If c^2 > a^2 + b^2, it's obtuse.
Why the other options are wrong
- A. Incorrect. An equilateral triangle has all sides equal, which is not the case here.
- B. Incorrect. For an acute triangle, c^2 < a^2 + b^2. Here, 13^2 = 169, while 7^2 + 8^2 = 49 + 64 = 113. 169 > 113.
- C. Incorrect. For a right triangle, c^2 = a^2 + b^2. Here, 169 ≠ 113.
Classifying Triangles by Angles (Sides)
Triangles can be classified as acute, right, or obtuse by comparing the square of the longest side (c^2) to the sum of the squares of the other two sides (a^2 + b^2).
- If c^2 < a^2 + b^2, the triangle is acute (all angles < 90°).
- If c^2 = a^2 + b^2, the triangle is right (one angle = 90°).
- If c^2 > a^2 + b^2, the triangle is obtuse (one angle > 90°).
Memory trick: Longest side squared, compare to others' sum, angles revealed!