Question

a triangle with sides 3, 4 and 6 is ____________
select one:
○ a. obtuse
○ b. right
○ c. acute

the hypotenuse of a 45-45-90 right triangle is $10\sqrt{2}$. the legs are ______
select one:
○ a. 20
○ b. none of these
○ c. $5\sqrt{2}$
○ d. 5
○ e. $\sqrt{2}$

Explanation:

Step1: Test triangle type (Q1)

Compare $c^2$ to $a^2+b^2$.
Let $a=3$, $b=4$, $c=6$.
$a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25$
$c^2 = 6^2 = 36$
Since $36 > 25$, $c^2 > a^2+b^2$.

Step2: 45-45-90 triangle leg formula (Q2)

Hypotenuse $= s\sqrt{2}$, solve for $s$.
Given hypotenuse $= 10\sqrt{2}$, so:
$s\sqrt{2} = 10\sqrt{2}$
Divide both sides by $\sqrt{2}$: $s = 10$
10 is not among options a,c,d,e.

Answer:

1. a. obtuse
2. b. none of these