Pythagoras Questions, Worksheets and Revision

The missing side is the longest side, thus the equation a^2+b^2=c^2 becomes:

8^2+14^2=c^2

Evaluating the two squares, we get,

c^2=64+196=260

Then, square rooting both sides of this equation, we get,

BC=\sqrt{260}=16.1\text{ cm (1 d.p.)}

To do this, we will plot the points on a graph, draw a line between them, and construct a right-angled with one side parallel to the x axis and another parallel to y axis. The resulting picture looks like:

We can see that the distance between the two points is the longest side of a right-angle triangle, so the equation a^2+b^2=c^2 becomes,

10^2+3^2=c^2

Evaluating the squares, we get

c^2=100+9=109

Finally, square rooting both sides, we get,

c=\sqrt{109}=10.4\text{ (3 s.f.)}

The missing side is the hypotenuse, thus the equation a^2+b^2=c^2 becomes:

5.9^2+6.7^2=c^2

Evaluating the two squares, we get,

c^2=34.81+44.89=79.7

Then, square rooting both sides of this equation, we get,

QR=\sqrt{79.7}=8.9\text{ cm (1 d.p.)}

Applying a rearranged form of Pythagoras, letting, a, be the missing length we want to find, then a^2=c^2-b^2 becomes, 

a^2=5.1^2-3.1^2

Evaluating the two squares, we get,

a^2=26.01-9.61=16.4

Then, square rooting both sides of this equation, we get,

a=\sqrt{16.4}=4.0\text{ cm (1 d.p.)}

Applying a rearranged form of Pythagoras, letting, a, be the length of the wall we want to find, then a^2=c^2-b^2 becomes, 

a^2=2.9^2-1.3^2

Evaluating the two squares, we get,

a^2=8.41-1.69=6.72

Then, square rooting both sides of this equation, we get,

a=\sqrt{6.72}=2.6\text{ cm (1 d.p.)}