Question

Use the Pythagorean Theorem to find the length of the leg in the triangle below. The figure shows a right triangle with one leg marked 3. The hypotenuse is marked 5.

Answer 1

4

Explanation:

Correct answers:

$4$

Let a represent the length of the leg and label a on the figure.

The figure shows a right triangle with legs marked a and 3. The hypotenuse is marked 5.

The figure shows a right triangle with legs marked a and 3. The hypotenuse is marked 5.

Using the Pythagorean Theorem with b=3, c=5, and solving for a, we have

a2+b2a2a2a2a2aa=c2=c2−b2=52−32=25−9=16=16−−√=4

The length of the leg is 4.

Answer 2

9514 1404 393

Answer:

4

Explanation:

If the unknown leg is represented by x, then the Pythagorean theorem tells you ...

x² + 3² = 5²

The sum of the squares of the legs equals the square of the hypotenuse.

Solving for x, we have ...

x² = 5² -3² = 25 -9 = 16

x = √16 = 4 . . . . . . . only the positive root is of interest

The missing leg length is 4 units.

_____

Additional comment

This exercise shows you that the triple (3, 4, 5) will form a right triangle. It is the smallest integer "Pythagorean triple", and the only one that is an arithmetic sequence (the differences between the numbers are the same). You will see this a lot, sometimes multiplied by various factors: 6, 8, 10, for example. It is worth remembering.