The question is an illustration of Pythagoras theorem
The value of q is [tex]\sqrt{ r^2 -84[/tex]
The given figure shows two right-angled triangles
Start by calculating the value of s using the following Pythagoras theorem
[tex]r^2 =s^2 + 10^2[/tex]
Evaluate 10^2
[tex]r^2 =s^2 + 100[/tex]
Subtract 100 from both sides
[tex]s^2 =r^2 - 100[/tex]
Take square roots of both sides
[tex]s =\sqrt{r^2 - 100[/tex]
Next, we calculate the value of q using the following Pythagoras theorem
[tex]q^2 = s^2 + 4^2[/tex]
Substitute [tex]s^2 =r^2 - 100[/tex]
[tex]q^2 = r^2 -100 + 4^2[/tex]
Evaluate 4^2
[tex]q^2 = r^2 -100 + 16\\[/tex]
Add -100 and 16
[tex]q^2 = r^2 -84[/tex]
Take square roots of both sides
[tex]q =\sqrt{ r^2 -84[/tex]
Hence, the value of q is [tex]\sqrt{ r^2 -84[/tex]
Read more about Pythagoras theorem at:
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