Question

which set of numbers can represent the side lengths, in inches, of an acute triangle?
○ 4, 5, 7
○ 5, 7, 8
○ 6, 7, 10
○ 7, 9, 12

Explanation:

Step1: Recall acute triangle rule

For a triangle with side lengths $a \leq b \leq c$, it is acute if $a^2 + b^2 > c^2$.

Step2: Test 4,5,7

$\text{Check } 4^2 + 5^2 \text{ vs } 7^2$
$16 + 25 = 41$, $7^2 = 49$, $41 < 49$ (obtuse)

Step3: Test 5,7,8

$\text{Check } 5^2 + 7^2 \text{ vs } 8^2$
$25 + 49 = 74$, $8^2 = 64$, $74 > 64$ (acute)

Step4: Verify remaining options (optional)

For 6,7,10: $36 + 49 = 85 < 100$ (obtuse)
For 7,9,12: $49 + 81 = 130 < 144$ (obtuse)

Answer:

B. 5, 7, 8