Carcass wrote:
The following are the measures of the sides of five different triangles. Which one of them represents a right triangle?
A. \(\sqrt{3}, \sqrt{4}, \sqrt{5}\)
B. 1,5,4,
C. 7,3,4
D. \(\sqrt{3},\sqrt{7},\sqrt{4}\)
E. 4,8,10
KEY CONCEPT: If a triangle is a right triangle, then it must be the case that a² + b² = c², where c = longest side, and a and b = other two sides. So, let's check each answer choice to see whether the side lengths meet the above condition.
A. Does (√3)² + (√4)² = (√5)²
In other words, does 3 + 4 = 5?
No.
ELIMINATE A
B. Does 1² + 4² = 5²
In other words, does 1 + 16 = 25?
No.
ELIMINATE B
C. Does 3² + 4² = 7²
In other words, does 9 + 16 = 49?
No.
ELIMINATE C
D. Does (√3)² + (√4)² = (√7)²
In other words, does 3 + 4 = 7?
YES!!!!!
Answer: D
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep