Question

The perimeter of an isosceles right triangle is 24 cm. How long are its sides?

Answer 1

@jim_thompson5910

Answer 2

@Nnesha @skullpatrol @mathmale

Answer 3

I thought of setting up an equation:
\(a + a + a\sqrt{2} = 24\)

Answer 4

What do you know about the hypotenuse?

Answer 5

This would be a 45-45-90 triangle I suppose

Answer 6

The length would be \(a\sqrt{2}\)?

Answer 7

Simpler than that. Just in general, what do you know about it?

Answer 8

It's the longest side of the triangle

Answer 9

Correct. By the way, is this multiple choice? I am pretty sure there is more than one answer.

Answer 10

Nope.

Answer 11

@jim_thompson5910 That's where I am having the problem.

Answer 12

Welp, you got this jim :D

Answer 13

I only get up \(2a + a\sqrt{2} = 24\). I don't know whether I should factor it to \(a(2 + \sqrt{2}) = 24\) and if I do then how would I solve for \(a\)?

Answer 14

why not factor out the GCF 'a' to go from
\[\Large a+a+a\sqrt{2} = 24\]
to
\[\Large a(1+1+\sqrt{2}) = 24\]

Answer 15

yes then you'd have
\[\Large a(2+\sqrt{2}) = 24\]

Answer 16

Would I divide both sides by \((2 + \sqrt{2})\)?

Answer 17

essentially the left side is saying `some number 'a' times (2+sqrt(2))`

Answer 18

yes you would divide both sides by (2+sqrt(2))

Answer 19

So now I would have \(a = \frac{24}{(2 + \sqrt{2})}\)

Answer 20

yep

Answer 21

That's the complete answer? Like no more simplifying?

Answer 22

you can rationalize the denominator if you want

Answer 23

or convert to decimal form to get an approximate answer