# How do you use the Pythagorean Theorem to find the missing side of the right triangle with the given measures given c is the hypotenuse and we have b=3x,c=7x?

##### 2 Answers

#### Explanation:

The Pythagorean Theorem states that

#a^2+b^2=c^2#

in a triangle with legs

With

#a^2+(3x)^2=(7x)^2#

Now, recall that when we have something like **both** the

#(3x)^2=3^2*x^2=9x^2#

Similarly, for

#(7x)^2=7^2*x^2=49x^2#

Substituting these back in to the Pythagorean Theorem equation, we see that

#a^2+9x^2=49x^2#

Subtract

#a^2=40x^2#

Take the square root of both sides.

#a=sqrt(40x^2)#

We can rewrite

#a=sqrt4*sqrt(x^2)*sqrt10#

#a=2xsqrt10#

#### Explanation:

Using the principle of proportionality disregard the

Think if it as working on a triangle that has been reduced in scale but is of the same ratio.

By Pythagoras

So

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Technically we could write

It is simpler just to leave it out for now but incorporate it at the end.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Scaling back up we have