Question

1. 7, 24, 25

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 rule

Verify sum of two sides > third side:
$7 + 24 > 25$ → $31 > 25$ (True)
$7 + 25 > 24$ → $32 > 24$ (True)
$24 + 25 > 7$ → $49 > 7$ (True)

Step2: Classify the triangle type

Use Pythagorean theorem: $a^2 + b^2 = c^2$ (right triangle test)
Calculate $7^2 + 24^2 = 49 + 576 = 625$
Calculate $25^2 = 625$

Answer:

Is it possible to form a triangle with these side lengths? Yes
Justify your answer:
$7 + 24 > 25$, $7 + 25 > 24$, $24 + 25 > 7$

If so, would the triangle be acute, right or obtuse? Right
Justify your answer:
The hypotenuse length we need: $\sqrt{7^2 + 24^2} = 25$
The hypotenuse length we have: $25$
What we have is equal to what we need, so the triangle is right.