FAN&MEDAL
Find the length of the hypotenuse of a triangle is side a = sqrt15 and side b = 2sqrt15. Do not use a calculator.

help? I have to do three of these

Question

FAN&MEDAL
Find the length of the hypotenuse of a triangle is side a = sqrt15 and side b = 2sqrt15. Do not use a calculator.

help? I have to do three of these

ccastudentgrade10 · Answer

*if side a

mathstudent55 · Answer

Since the triangle has a hypotenuse, what kind of triangle is it?

ccastudentgrade10 · Answer

its a right triangle @mathstudent55

ccastudentgrade10 · Answer

i just don't know how to solve it without a calculator

mathstudent55 · Answer

Since you know it's a right triangle, you can use the Pythagorean theorem.

$a^2 + b^2 = c^2$

Use the two given sides as a and b, and solve for c.

mathstudent55 · Answer

$a^2 + b^2 = c^2$

First, copy the equation above.
Now rewrite the equation, but replace a with $\sqrt{15}$, and replace b with $2\sqrt{15} $.
What do you have now?

ccastudentgrade10 · Answer

would it be 15 + 30 = c^2?

ccastudentgrade10 · Answer

so then sqrt45 would be the answer

mathstudent55 · Answer

No.

mathstudent55 · Answer

First just replace a and b by their values.
Then calculate.

mathstudent55 · Answer

$a^2 + b^2 = c^2$

$(\sqrt{15})^2 + (2\sqrt{15})^2= c^2$

You see how the substitution into the formula is done?

ccastudentgrade10 · Answer

oh okay. but the sqrt15^2 just becomes 15, right?

mathstudent55 · Answer

When you square $\sqrt {15} $, you do get 15.

When you square $2 \sqrt {15} $, you must also square the 2.

mathstudent55 · Answer

$(\sqrt{15})^2 + (2\sqrt{15})^2= c^2$

$15 + 2^2 (\sqrt{15})^2 = c^2$

$15 + 4 \times 15 = c^2$

The 2 is also squared.

ccastudentgrade10 · Answer

OH okay

ccastudentgrade10 · Answer

so 15 + 60 = c^2
75 = c^2
75^2 = c

mathstudent55 · Answer

No.
You are correct up to here:

$75 = c^2$

Now you take square roots of both sides.
We can also switch sides first to have the variable on the left.

$c^2 = 75$

Take square roots. We will only use the positive square root of 75 since we are dealing with the length of a side of a triangle which cannot be negative.

$c = \sqrt {75} $

Ok so far?

mathstudent55 · Answer

There is one final step we can do.
We can simplify the square root.
We need to factor out a perfect square number out of 75.

ccastudentgrade10 · Answer

okay

ccastudentgrade10 · Answer

my teacher says 75^2 is fine, i can just leave the answer squared

mathstudent55 · Answer

$c = \sqrt {75} = \sqrt{25 \times 3} = \sqrt{25}\sqrt{3} = 5 \sqrt 3$

ccastudentgrade10 · Answer

thank you!!

mathstudent55 · Answer

75^2 is completely incorrect.
You can leave the answer as sqrt(75), or $\sqrt {75} $, but not as $75^2$

mathstudent55 · Answer

You're welcome.