Converse of the Pythagorean Theorem Worksheet

**Page 3**

21.

A Pythagorean triplet when multiplied by a positive integer $n$ is also a Pythagorean triplet. State whether the statement is true or false.

a. | True | ||

b. | False |

Multiply each number by

Then the new set is 9

(15

[Apply Pythagorean theorem.]

225

[Simplify.]

225

A Pythagorean triplet when multiplied by a positive integer

Correct answer : (1)

22.

The radius of the circle is 3 inches. Find the length of the sides of the square using the Pythagorean theorem.

a. | 3$\sqrt{2}$inches | ||

b. | 3 inches | ||

c. | 6$\sqrt{2}$ inches | ||

d. | 6 inches |

BD is the diameter, BD = 6 inches.

[Diameter = 2 × radius.]

From right triangle BDC, BD

[Apply Pythagorean theorem.]

BD

[Since all sides of a square are equal,replace CD with BC.]

6

[Substitute BD.]

36 = 2BC

[Simplify.]

BC

[Divide by 2 on both sides]

BC =

[Take square root of both sides.]

The length of side of square = 3

Correct answer : (1)

23.

The perimeter of a right triangle is 150 inches and the ratio of the lengths of the 2 legs is 5 : 12. Find the length of the hypotenuse.

a. | 13 inches | ||

b. | 25 inches | ||

c. | 60 inches | ||

d. | 65 inches |

Let the length of two legs be 5

Hypotenuse

[Apply Pythagorean theorem.]

Hypotenuse

[Apply exponents .]

= 169

[Simplify.]

Hypotenuse =

[Take square root of both sides.]

Perimeter of right triangle = 150 inches.

Perimeter of the right triangle = 5

30

[Equate perimeters]

[Divide by 30 on both sides.]

Hypotenuse = 13

[Substitute

The length of hypotenuse = 65 inches.

Correct answer : (4)

24.

The length of the chord AB = 10 in. What is the radius of the circle?

a. | 5 in | ||

b. | 5$\sqrt{2}$ in | ||

c. | 6$\sqrt{2}$ in | ||

d. | 6 in |

AOB is a right triangle.

AB

[Apply Pythagorean theorem.]

AB

[Since, the radius of the circle = OA = OB.]

OA

[Divide by 2 on both sides.]

OA

[Substitute AB.]

OA

[Apply exponents and simplify.]

OA =

[Find the positive square root.]

The radius of the circle is 5

Correct answer : (2)

25.

State which of the following measures will form a right triangle?

(i) 9, 12, 15

(ii) 2, 4, $\sqrt{20}$

(iii) 3, 4, 6

(i) 9, 12, 15

(ii) 2, 4, $\sqrt{20}$

(iii) 3, 4, 6

a. | (i) only | ||

b. | (ii) only | ||

c. | (iii) only | ||

d. | both (i) and (ii) |

In (i), 15

225 = 81 + 144 = 225

The measures 9, 12 and 15 will form a right triangle.

= 4 + 16 = 20

In (ii), (

So, the measures 2, 4 and

Applying Pythagorean theorem for (iii), 6

36 = 9 + 16 = 25, 36 is not equal to 25.

The measures 3, 4 and 6 cannot form a right triangle.

So, (i) and (ii) only will form right triangles.

Correct answer : (4)

26.

Which of the figures is a right triangle?

a. | Only Figure 1 | ||

b. | Only Figure 2 | ||

c. | Only Figure 3 | ||

d. | Both Figures 2 & 3 |

Applying Pythagorean theorem for figure (1), 6

Since 36 ≠ 25, figure (1) is not a right triangle.

Applying Pythagorean theorem for figure (2), 10

100 = 100

So, figure (2) is a right triangle.

Applying Pythagorean theorem for figure (3), 4

Since 16 ≠ 8, figure (3) is not a right triangle.

Only figure (2) is the right triangle

Correct answer : (2)

27.

Jeff walked diagonally across a square garden with each side measuring 25 ft long (from one corner to the opposite corner). How far did he walk?

a. | 37.47 ft | ||

b. | 33.23 ft | ||

c. | 35.35 ft | ||

d. | 35.47 ft |

All the angles of a square are right angles. So, the diagonal of the square will be the hypotenuse of the right triangle formed by two adjacent sides and the diagonal.

[Apply Pythagorean theorem.]

[Substitute

[Apply exponents and simplify.]

[Take square root on both sides.]

The total distance Jeff walked is 35.35 ft.

Correct answer : (3)

28.

If one side of a right triangle is two times the other and the length of hypotenuse is 10 ft, then what are the measures of the two sides?

a. | 2 ft and 4 ft | ||

b. | 3 ft and 5 ft | ||

c. | 2$\sqrt{5}$ ft and 4$\sqrt{5}$ ft | ||

d. | 3$\sqrt{5}$ ft and 4$\sqrt{5}$ ft |

[One side is two times the other.]

[Apply Pythagorean theorem.]

5

[Divide by 5 on both sides.]

[Take square root on both sides.]

The other side = 2

[Substitute

The two sides are 2

Correct answer : (3)