Pythagorean Theorem Challenge Quiz

Question 1

A rectangular prism has side lengths $3$, $4$, and $12$. What is the length of its space diagonal?

Accepted Answer

$13$

Answer

$\sqrt{73}$

Answer

$\sqrt{121}$

Answer

$19$

Question 2

A rectangular box is $2$ m by $3$ m by $6$ m. A spider starts at one corner and wants the shortest path along the surface to the opposite corner. What is the shortest distance?

Accepted Answer

$\sqrt{61}$

Answer

$\sqrt{97}$

Answer

$7$

Answer

$\sqrt{73}$

Question 3

Conceptual: Which statement best explains why the Pythagorean theorem $a^2+b^2=c^2$ is true for right triangles?

Accepted Answer

It is true because the areas of squares built on the legs add to the area of the square built on the hypotenuse.

Answer

It is true because the hypotenuse is always twice the length of a leg, so $c^2=4a^2$ and must equal $a^2+b^2$.

Answer

It is true because $a+b=c$ in any right triangle, and squaring both sides gives $a^2+b^2=c^2$.

Answer

It works because the triangle has three sides, and any three side lengths satisfy $a^2+b^2=c^2$.

Pythagorean Theorem Challenge Quiz

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