Pythagorean Theorem Worksheet

**Page 1**

1.

Pythagorean theorem is applicable for ________.

a. | obtuse triangles only | ||

b. | any triangle | ||

c. | right triangles only | ||

d. | None of the above |

Correct answer : (3)

2.

What is the length of the side PR of ΔPQR in the figure?

a. | $\sqrt{20}$ in. | ||

b. | $\sqrt{50}$ in. | ||

c. | 25 in. | ||

d. | 5 in. |

From the figure, PQ = 5 in. and QR = 5 in.

According to Pythagorean theorem, in a right triangle, square of the hypotenuse = sum of the squares of the other two sides.

In ΔPQR, PR is hypotenuse.

From ΔPQR, PR

PR

PR =

The length of the side PR =

Correct answer : (2)

3.

What is the length of the side PR in the right triangle?

PR

PR

a. | √41 units | ||

b. | 10 units | ||

c. | √21 units | ||

d. | 20 units |

PQR is a right triangle and PR is the hypotenuse.

Applying Pythagorean theorem for ΔPQR, PR

PR

[Substitute PQ = 5 and QR = 4.]

PR

PR = √41

[Take square root on both the sides.]

So, the length of the side PR is √41 units.

Correct answer : (1)

4.

What is the length of the third side of the triangle in the figure?

a. | $\sqrt{8}$ units | ||

b. | 4 units | ||

c. | $\sqrt{15}$ units | ||

d. | $\sqrt{34}$ units |

The side opposite to the right angle is hypotenuse.

Let

Applying Pythagorean theorem,

[Evaluate powers and add.]

[Take square root on both the sides.]

The third side of the triangle is √34 units.

Correct answer : (4)

5.

What are the values of $x$ and $y$ in the triangle?

a. | 24 units and 45 units | ||

b. | 4 units and 15 units | ||

c. | 2√5 units and 45 units | ||

d. | √160 units and √41 units |

BC

[Apply Pythagorean theorem.]

[Substitute BC, BD and CD.]

[Evaluate powers and simplify.]

[Take square root both sides.]

ΔADC is a right triangle.

AC

[Apply Pythagorean theorem.]

[Substitute AC, AD and CD.]

[Evaluate powers and simplify.]

[Take square root both sides.]

Correct answer : (4)

6.

Which of the following measures make a right triangle?

a. | 7 cm, 24 cm, 25 cm | ||

b. | 3 cm, 4 cm, 7 cm | ||

c. | 8 cm, 24 cm, 25 cm | ||

d. | 5 cm, 12 cm, 14 cm |

Correct answer : (1)

7.

Find the length of the side PR in the ΔPQR shown.

a. | 25 in. | ||

b. | $\sqrt{20}$ in. | ||

c. | 5 in. | ||

d. | $\sqrt{50}$ in. |

Correct answer : (4)

8.

P is a point in the interior of the rectangle ABCD. AP = 15 units, CP = 5 units and DP = 8 units . What is the value of $\stackrel{\u203e}{\mathrm{BP}}$?

a. | 9.3 units | ||

b. | 12 units | ||

c. | $\sqrt{264}$ units | ||

d. | $\sqrt{186}$ units |

MN is drawn || to AB through P.

BM = AN =

[Figure.]

BPÃ‚Â² = MPÃ‚Â² + BMÃ‚Â² =

[Pythagorean Theorem.]

CPÃ‚Â² = MPÃ‚Â² + CMÃ‚Â² ; 25 =

[Pythagorean Theorem.]

DPÃ‚Â² = DNÃ‚Â² + PNÃ‚Â² ; 64 =

[Pythagorean Theorem.]

APÃ‚Â² = ANÃ‚Â² + PNÃ‚Â² ; 225 =

[Pythagorean Theorem.]

[Simplify using steps 5, 6 and 7.]

= 225 + 25 - 64 = 186.

So, BP =

[Steps 4 and 9.]

Correct answer : (4)

9.

The perimeter of a right triangle is 48 units . The sum of the squares of all the sides is 800 sq.units. What is the area of the triangle?

a. | 116 sq.units | ||

b. | 96 sq.units | ||

c. | 106 sq.units | ||

d. | 111 sq.units |

Sum of squares =

[Pythagorean theorem.]

[Simplify.]

[Given.]

[Squaring on both sides.]

2

[Substitute the value of

Area of the triangle =

Correct answer : (2)

10.

The perimeter of a right triangle is 108 cm and the sum of the squares of its sides is 4050 sq.cm. Find the length of the smallest side.

a. | 36 cm | ||

b. | 44.36 cm | ||

c. | $\frac{75}{2}$cm | ||

d. | 27 cm |

[Apply Pythagorean theorem.]

2

[Add

[Divide by 2 on both sides.]

[Take square root of both sides.]

[Substitute

[Square on both sides.]

2025 + 2

[Substitute

[Divide by 2 on both sides.]

[From step 7 and step 10.]

So,

[Solve for

So, the length of the smallest side is 27 cm.

Correct answer : (4)