Question

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

Explanation:

Step1: Recall acute triangle rule

For sides $a \leq b \leq c$, triangle is acute if $a^2 + b^2 > c^2$.

Step2: Test 6,7,10

$6^2 + 7^2 = 36 + 49 = 85$; $10^2 = 100$. $85 < 100$ (obtuse)

Step3: Test 4,5,7

$4^2 + 5^2 = 16 + 25 = 41$; $7^2 = 49$. $41 < 49$ (obtuse)

Step4: Test 5,7,8

$5^2 + 7^2 = 25 + 49 = 74$; $8^2 = 64$. $74 > 64$ (acute)

Step5: Test 7,9,12

$7^2 + 9^2 = 49 + 81 = 130$; $12^2 = 144$. $130 < 144$ (obtuse)

Answer:

C. 5, 7, 8