Question

a triangle has vertices at (0, 0), (3, 0), and (3, 4). what is the hypotenuse of the triangle?
a. 5 units
b. $\sqrt{9}$ units
c. $\sqrt{12}$ units
d. $\sqrt{16}$ units

Explanation:

Step1: Identify right angle vertex

The triangle has vertices (0,0), (3,0), (3,4). The right angle is at (3,0) since (3,0)-(0,0) is horizontal and (3,4)-(3,0) is vertical.

Step2: Calculate leg lengths

Leg 1: Distance between (0,0) and (3,0) is $3-0=3$ units.
Leg 2: Distance between (3,0) and (3,4) is $4-0=4$ units.

Step3: Apply Pythagorean theorem

Hypotenuse $c = \sqrt{a^2 + b^2} = \sqrt{3^2 + 4^2} = \sqrt{9+16} = \sqrt{25}=5$ units.

Answer:

a. 5 units