Question

1. 6, 8, 10

is it possible to form a triangle with these side lengths?
justify your answer:

if so, would the triangle be acute, right or obtuse?
justify your answer:
the hypotenuse length we need:
the hypotenuse length we have:
what we have is what we need, so the triangle is .

Explanation:

Step1: Check triangle inequality

Verify sum of two shortest sides:
$6 + 8 = 14$
Compare to longest side: $14 > 10$

Step2: Confirm triangle possibility

All triangle inequalities hold:
$6+10>8$, $8+10>6$, $6+8>10$

Step3: Test triangle type (Pythagorean theorem)

Calculate sum of squares of legs:
$6^2 + 8^2 = 36 + 64 = 100$
Calculate square of longest side:
$10^2 = 100$

Step4: Match to triangle classification

Compare the two results: $100 = 100$

Answer:

Is it possible to form a triangle with these side lengths? $\boldsymbol{Yes}$
Justify your answer:
$6 + 8 > 10$ (all triangle inequalities are satisfied)

If so, would the triangle be acute, right or obtuse? $\boldsymbol{Right}$
Justify your answer:
The hypotenuse length we need: $\boldsymbol{10}$
The hypotenuse length we have: $\boldsymbol{10}$
What we have is $\boldsymbol{equal\ to}$ what we need, so the triangle is $\boldsymbol{right}$.