A right triangle has legs of length 5 and 12. What is its area?
- A17
- B26
- C30
- D60
- E65
Right triangle area: use the legs, not the hypotenuse
Try it before you scroll. Two minutes on the clock, then commit to an answer.
Correct answer: C
In a right triangle the two legs are perpendicular, so one leg serves as the base and the other as the height:
Area = (1/2) × 5 × 12 = 30.
You can confirm the triangle is coherent with the Pythagorean theorem: 5² + 12² = 25 + 144 = 169 = 13², so the hypotenuse is 13. That fact is a check, not a requirement for the area.
The traps:
- (D), 60, forgets the 1/2 in the area formula.
- (A), 17, adds the legs.
- (B), 26, doubles the hypotenuse.
- (E), 65, multiplies a leg by the hypotenuse (5 × 13), a hint that the test writer expects you to compute 13 first and then misuse it.
Memorize the common Pythagorean triples (3-4-5, 5-12-13, 8-15-17, 7-24-25). They appear constantly and save a minute each time.