Question

for which of these shapes is it possible to apply the pythagorean theorem directly?
a. circle
b. right triangle
c. equilateral triangle
d. square

Explanation:

The Pythagorean Theorem ($a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs of a right - triangle and $c$ is the hypotenuse) is specifically defined for right - triangles. A circle has properties related to radius, diameter, circumference, and area (using formulas like $C = 2\pi r$ or $A=\pi r^{2}$). An equilateral triangle has all sides equal and angles equal to $60^{\circ}$, and its side - length relationships are based on trigonometric ratios for $60^{\circ}$ angles (e.g., height $h=\frac{\sqrt{3}}{2}s$ where $s$ is the side - length). A square has properties related to side - length and area ($A = s^{2}$) or diagonal ($d=\sqrt{2}s$), but the Pythagorean Theorem is not directly applied in the same fundamental way as in a right - triangle.

Answer:

B. Right triangle