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CanadaON
Grade 8

8.03 Finding a shorter side

Worksheet
Unknown sides
1

Find the number that completes a Pythagorean triple given the following:

a

The two largest numbers are 10 and 8.

b

The largest and smallest numbers are 41 and 9.

2

For the following right-angled triangles:

i

Write the equation that the sides of the triangle satisfy.

ii

Solve the equation to find the length of the unknown side.

a
b
3

Explain how to find the length of the unknown side in the following triangle.

4

Find the length of the unknown side of the following triangles:

a
b
c
d
e
f
5

Find the length of the unknown side of the following triangles, correct to two decimal places:

a
b
c
d
e
f
g
h
6

Find the length of the unknown side of the following triangles, giving your answer as a surd:

a
b
7

The two short sides of a triangle have lengths of 10 and 17. Sarah notices that she can divide the triangle into two smaller right-angled triangles, each with a height of 8.

a

Find the base lengths of the two right-angled triangles.

b

Find the base length of the original triangle.

8

Find the base length of the following triangles:

a
b
Perimeter
9

Consider a right-angled triangle with hypotenuse of length 15 \,\text{cm} and another side of length 4 \,\text{cm}.

a

Find the length of the other side, correct to two decimal places.

b

Find the perimeter, correct to two decimal places.

10

Consider a rectangle with a diagonal of length 25 \,\text{cm} and a side of length 24 \,\text{cm}.

a

Find the length of the other side.

b

Find the perimeter.

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Outcomes

8.E2.4

Describe the Pythagorean relationship using various geometric models, and apply the theorem to solve problems involving an unknown side length for a given right triangle.

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