Exercises: Pythagorean theorem - ACT Math

A

Recall / Warm-Up

1.

What is $\sqrt{144}$ ?

A.

11

B.

12

C.

14

D.

72

2.

In a right triangle, which side is always the longest?

A.

The base

B.

The height

C.

The hypotenuse

D.

It depends on the triangle

3.

Evaluate: $6^2 + 8^2$ .

A.

48

B.

100

C.

14

D.

196

B

Fluency Practice

C

Varied Practice

D

Word Problems / Application

1.

A rectangular TV screen is 36 inches wide and 48 inches tall. What is the length of the diagonal, in inches?

2.

A 17-foot ladder leans against a wall with its base 8 feet from the wall. How high up the wall does the ladder reach?

A.

9 feet

B.

15 feet

C.

$\sqrt{353}$ feet

D.

25 feet

3.

An isosceles triangle has two equal sides of length 13 and a base of length 10.

1.

What is the height of the triangle?

2.

What is the area of the triangle?

4.

Find the distance between the points (1, 2) and (4, 6).

E

Error Analysis

1.

Marcus solved this problem:

"A right triangle has legs 5 and 12. Find the hypotenuse."

Marcus's work:

$c^2 = 5^2 + 12^2 = 25 + 144 = 169$
$c = 169$

What error did Marcus make, and what is the correct hypotenuse?

A.

Marcus forgot to take the square root. The correct hypotenuse is $c = 13$ .

B.

Marcus should have subtracted. The correct hypotenuse is $c = \sqrt{119}$ .

C.

Marcus's answer of 169 is correct.

D.

Marcus squared incorrectly. The correct hypotenuse is $c = \sqrt{170}$ .

2.

Priya solved this problem:

"A right triangle has sides 9, 15, and 12. Find the hypotenuse."

Priya's work:

$c = \sqrt{9^2 + 15^2}$
$c = \sqrt{81 + 225}$
$c = \sqrt{306}$

What error did Priya make, and what is the correct hypotenuse?

A.

Priya used 15 as a leg instead of the hypotenuse. The hypotenuse is 15.

B.

Priya should have subtracted. The correct hypotenuse is $\sqrt{144} = 12$ .

C.

Priya's answer of $\sqrt{306}$ is correct.

D.

Priya forgot to include side 12. The correct hypotenuse is $\sqrt{450}$ .

F

Challenge / Extension

1.

Find the distance between the points $(-2, 3)$ and $(6, 9)$ .

2.