Pythagoras: finding a shorter side

Difficulty Stretch · Set 3ryoq8

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1
The triangle has a right angle and its longest side is 34 m. How long is the side marked ?, in m?
2
The triangle has a right angle and its longest side is 13 cm. How long is the side marked ?, in cm?
3
The triangle has a right angle and its longest side is 10 mm. How long is the side marked ?, in mm?
4
The triangle has a right angle and its longest side is 26 cm. How long is the side marked ?, in cm?
5
The triangle has a right angle and its longest side is 41 m. How long is the side marked ?, in m?
6
The triangle has a right angle and its longest side is 20 cm. How long is the side marked ?, in cm?
7
The triangle has a right angle and its longest side is 41 mm. How long is the side marked ?, in mm?
8
The triangle has a right angle and its longest side is 10 cm. How long is the side marked ?, in cm?
9
The triangle has a right angle and its longest side is 34 m. How long is the side marked ?, in m?
10
The triangle has a right angle and its longest side is 17 cm. How long is the side marked ?, in cm?
11
The triangle has a right angle and its longest side is 41 cm. How long is the side marked ?, in cm?
12
The triangle has a right angle and its longest side is 34 mm. How long is the side marked ?, in mm?
13
The triangle has a right angle and its longest side is 20 mm. How long is the side marked ?, in mm?
14
The triangle has a right angle and its longest side is 41 mm. How long is the side marked ?, in mm?
15
The triangle has a right angle and its longest side is 25 mm. How long is the side marked ?, in mm?
16
The triangle has a right angle and its longest side is 20 mm. How long is the side marked ?, in mm?
17
The triangle has a right angle and its longest side is 25 mm. How long is the side marked ?, in mm?
18
The triangle has a right angle and its longest side is 10 m. How long is the side marked ?, in m?
19
The triangle has a right angle and its longest side is 26 mm. How long is the side marked ?, in mm?
20
The triangle has a right angle and its longest side is 5 m. How long is the side marked ?, in m?

What is in this set

The numbers in this set run from 4 to 41.
A careful solution takes 3 written steps on average.
The mistake this set invites most often, in 100% of the problems: the two sides were subtracted; it is the squares that are subtracted, and then the square root is taken.
Answers are a whole number.

Drawing 240 problems from this page produced 36 different ones, 15% — so a sheet of 20 will come back to a problem you have seen — there are only so many sensible ones of this kind.

The same skill, harder or easier

We would put this in front of a grade 8 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.