Question

Please help me with this one. The base of an isosceles triangle and the altitude drawin from one of the congruent sides are equal to 18cm and 15cm, respectively. Find the lengths of the sides of the triangle.

Answer 1

Let's start with the basics, What's our shape?

Answer 2

It's an isosceles triangle.

Answer 3

ok good now...

Answer 4

Sorry if it takes me too long sometimes to reply, connection's kinda crappy at this moment. :/

Answer 5

With an isosceles triangle
What's the rules?
What do we know about the two sides?
And its ok. :)

Answer 6

Ok, we know that An isosceles triangle is a triangle with two equal sides.

Answer 7

Uhm, two sides of that triangle are equal?

Answer 8

That's okay
Thanks for telling me what's going on your end
My connection sometimes fails as well.

Answer 9

Yup, that's right!

Answer 10

What do we know about the base?
What is the length of the base?

Answer 11

The base is 18cm.

Answer 12

Awesome!

Answer 13

And the 2nd number is height
Right?

Answer 14

which is 15cm

Answer 15

Right, and it is 15cm. :)

Answer 16

Now, We are asked to solve for the sides
Have you learned about the Pythagorean theorem?

Answer 17

\[C^2 \sqrt{a^2+b^2}\]

Answer 18

C (the hypotenuse) does look like that
It is normally a^2 + b^2 = c^2
The ^ sign means exponent
So with your set up
You removed the middle man
And put down the square root immediately
Now with that in mind
We need to set up a right triangle, to solve for c.

Answer 19

Yup, I'm familiar. And, only if it's a right triangle that we can use that equation. :)

Answer 20

What's our height of the right triangle?
Keep in mind

Answer 21

The right triangle is 1/2 the isosceles.
Now, that base
I mentioned that the right triangle is half for a reason. This part is the reason
What'll be the base of the right triangle?
18 is the base for the isosceles triangle
The right triangle is half of the isosceles triangle
It's cut in half, so that would be 9.
With that done
We can plug in the 9 and 15 into a and b
And solve for c

Answer 22

\[\sqrt{15^2+9^2}= 17.50\]

Answer 23

The height is 15. Base is 9. it would be 15^2+9^2=c^2

Answer 24

Then sqrt the answer, right?

Answer 25

Yes. Do you have any questions now?

Answer 26

17.50 is our final answer. :)

Answer 27

The original answer is 17.4928.. round it off= 17.50. Are you clear with that?

Answer 28

Yes, yes. Thank you very much! I'm kinda new here, but people here are awesome. Haha. Thank you for your help. :)

Answer 29

Not a problem, and welcome to open study. I wish you all the best!