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Pythagorean Theorem Exercises

This document contains 14 math word problems involving the Pythagorean theorem. The problems involve finding missing lengths of sides in right triangles, calculating perimeters and diagonals, determining if a triangle is a right triangle based on side lengths, and solving for unknown variables. The answers provided give the numerical solutions to each problem, rounded to the specified decimal places.

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Branson Kaution Peters II
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841 views4 pages

Pythagorean Theorem Exercises

This document contains 14 math word problems involving the Pythagorean theorem. The problems involve finding missing lengths of sides in right triangles, calculating perimeters and diagonals, determining if a triangle is a right triangle based on side lengths, and solving for unknown variables. The answers provided give the numerical solutions to each problem, rounded to the specified decimal places.

Uploaded by

Branson Kaution Peters II
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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PYTHAGORAS WORKSHEET

1) Find the hypotenuse of the following triangles.


a 12cm
8cm c 9cm
15cm 6cm
b d
8cm 12cm
16cm
2) Using Pythagoras, find the lengths of the sides labelled with letters.
15cm 5cm
b c 12cm
a 17cm 4cm 20cm
12cm d 13cm

3) Find the missing lengths of the triangles below. If necessary, round


answers to 1 decimal place.
8cm 6cm
3.4cm a
9cm b 17cm 10cm c

1.9cm e
d 15cm 9cm 20cm f
2.4cm
16cm
4) Find the perimeter of the following triangles;

c
a 12cm b 6cm 13cm 12cm
10cm
16cm 8cm 15cm

d
5) The triangle DEF is shown below. Find the length of EF to 1 decimal
place.
D

7.9cm 8.9cm

E F
6) To wash a window that is 8 metres off the ground, Ben leans a 10 metre
ladder against the side of the building. To reach the window, how far
from the building should Ben place the base of the ladder?
7) A rectangular swimming pool is 21 metres wide and 50 metres long.
Calculate the length of the diagonal to 1 decimal place.
8) Miss Barker is teaching a 5th grade class. She is standing 12 feet in front
of Jim. Francisco is sitting 5 feet to Jim’s right. How far apart are Miss
Barker and Francisco?
9) A triangle has sides with lengths of 10 metres, 16 metres and 20 metres.
Is it a right angled triangle? Explain your reasoning.
10) a) One side of a right angled triangle is 10cm. The other two are both of
length x. Calculate x to 2 decimal places.
b) Find the perimeter of the triangle in part a)
11) Find the length of the diagonal of a square of side 4cm to 2 decimal
places.
12) The diagram below shows a shaded parallelogram drawn inside a
rectangle. Using Pythagoras, find the hypotenuse of triangle A and the
hypotenuse of triangle B to 1 decimal place.
3cm

A
5cm
B

3cm
10cm
13) Here is a trapezium, use Pythagoras’ Theorem to find the value of k to 1
decimal place.
K cm

20cm 22cm

30cm
14) The following triangle is NOT a right angled triangle and so you cannot
apply Pythagoras’ theorem directly. Find the length of x to 2 d.p.

x x 35cm

100cm
Answers:
1) a = 17cm b = 10cm c = 15cm d = 20cm
2) a =8cm b =3cm c =16cm d =5cm
3) a =9.6cm b =15cm c =8cm d =3.1cm e =12cm f =12cm
4) a =48cm b =24cm c =30cm d =40cm
5) EF = 16.8cm
6) 6 metres
7) 54.2 metres
8) 13 ft
9) No. Using Pythagoras, 𝑎2 + 𝑏 2 ≠ 𝑐 2 (a squared + b squared does not
equal hypotenuse squared)
10) a) x = 7.07cm b) perimeter = 24.14 cm
11) 5.65 cm
12) A = 5.8cm B = 5.8cm
13) k = 20.8cm
14) x= 61.03 cm

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