Pythagorean Theorem practice worksheet with multiple-choice questions and diagrams.

Here are the step-by-step solutions for the questions in the worksheet.

Question 1

Problem: Find the length of the missing side (hypotenuse) of a right triangle with legs $20\text{ cm}$ and $48\text{ cm}$.

1. Identify the sides: The legs ($a$ and $b$) are $20$ and $48$. The missing side is the hypotenuse ($c$).
2. Use the Pythagorean Theorem: $a^2 + b^2 = c^2$.
3. Square the legs:
* $20^2 = 400$
* $48^2 = 2,304$
4. Add them together: $400 + 2,304 = 2,704$.
5. Find the square root of $2,704$ to get $c$: $\sqrt{2,704} = 52$.

The missing side is 52 cm.

Question 2

Problem: The Pythagorean Theorem ONLY works on which triangle?

The Pythagorean Theorem ($a^2 + b^2 = c^2$) describes the relationship between the sides of a specific type of triangle. It only applies when there is a $90$-degree angle (a right angle).

The correct answer is a right triangle.

Question 3

Problem: The Pythagorean Theorem is $a^2 + b^2 + c^2$. True or False?

The actual formula for the Pythagorean Theorem is $a^2 + b^2 = c^2$ (where $c$ is the hypotenuse). The statement in the question adds all three squares together, which is incorrect.

The statement is false.

Question 4

Problem: Find the missing side $b$. The hypotenuse is $78$, and one leg is $30$.

1. Identify the sides: Hypotenuse ($c$) = $78$, Leg ($a$) = $30$, Missing Leg ($b$) = ?
2. Rearrange the formula to solve for a leg: $b^2 = c^2 - a^2$.
3. Square the known numbers:
* $78^2 = 6,084$
* $30^2 = 900$
4. Subtract: $6,084 - 900 = 5,184$.
5. Find the square root: $\sqrt{5,184} = 72$.

The missing side is 72.

Question 5

Problem: Find the missing side $c$ (hypotenuse). The legs are $5$ and $4$.

1. Identify the sides: Legs ($a$ and $b$) are $5$ and $4$. Missing side is hypotenuse ($c$).
2. Use the formula: $a^2 + b^2 = c^2$.
3. Square the legs:
* $5^2 = 25$
* $4^2 = 16$
4. Add them together: $25 + 16 = 41$.
5. So, $c^2 = 41$. To find $c$, you would take the square root ($\sqrt{41} \approx 6.4$). Looking at the options, $6.4$ is the decimal approximation of $\sqrt{41}$.

The missing side is approximately 6.4.

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Final Answer:
1. B
2. C
3. A
4. B
5. B