Question

Quilt squares are cut on the diagonal to form triangular quit pieces. The hypotenuse of the resulting triangles is 34 inches long. What is the side length of each piece?

Answer 1

@whpalmer4 can you help me ?

Answer 2

Okay, this problem is the exact opposite of the problem we just did. If you have a square and cut it diagonally, the hypotenuse is exactly \(\sqrt{2}\) times the length of the sides of the square.

Answer 3

If the length of the side is \(s\), \[34 = s\sqrt{2}\]Can you solve for the value of \(s\)?

Answer 4

im confused

Answer 5

Okay, tell me what is confusing you...

Answer 6

\[s^2 + s^2 = 34^2\]

Answer 7

the whole 34 = 8 \[\sqrt{2}\]

Answer 8

\[1^2 + 1^2 = c^2\]\[1+1=c^2\]\[2=c^2\]\[\sqrt{2} = c\]

So, in such a triangle (diagonal of a square), the hypotenuse is always \(\sqrt{2}\) times the length of the side.

We know the hypotenuse of this triangle is 34. We therefore know that \[s\sqrt{2} = 34\]where \(s\) is the length of a side of the square.

\[s\sqrt{2} = 34\]\[\frac{s\sqrt{2}}{\sqrt{2}} = \frac{34}{\sqrt{2}}\]\[s = \frac{34}{\sqrt{2}}\]

Answer 9

its not 34 radical of 2 is it ?

Answer 10

How can the legs of a right triangle be longer than the hypotenuse?!? The hypotenuse is the longest side of the triangle.

\(\sqrt{2}\approx 1.414\) so anything you multiply by it gets larger, not smaller.

Answer 11

would it be 17 radical 2 ?

Answer 12

Do you know how to rationalize radical expressions?

Answer 13

\[\frac{34}{\sqrt{2}}\]is a radical expression with a radical in the denominator. When we rationalize it, we remove the radical from the denominator by multiplying both numerator and denominator by the denominator. That's just a fraction that equals 1, so it doesn't change the value at all:

\[\frac{34}{\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}} = \frac{34\sqrt{2}}{\sqrt{2}*\sqrt{2}}\]Can you simplify that any more?

Answer 14

yes ?

Answer 15

Okay, please do so!

Answer 16

I cant remember how to simplify that

Answer 17

what is \(\sqrt{2}*\sqrt{2}=\)

Answer 18

1 ?

Answer 19

do you remember what I said the value of \(\sqrt{2}=\)

Answer 20

1

Answer 21

No. Scroll back and read.

Answer 22

1.414

Answer 23

in case you don't know, \(\approx\) means "approximately" — the value of the square root of 2 is a never-ending string of digits, so I can't write \(\sqrt{2} = 1.414...\) because I couldn't write them all down.

Answer 24

Right. So what is \(1.414*1.414=\)

Answer 25

1.999396

Answer 26

you there ?

Answer 27

yes, what number is that very close to?

Answer 28

\[\sqrt{2}*\sqrt{2} = 2\]The definition of the square root of 2 is that number which when multiplied by itself gives you 2.

\[\frac{34*\sqrt{2}}{\sqrt{2}*\sqrt{2}} = \frac{34*\sqrt{2}}{2} = 17\sqrt{2}\]

Answer 29

You seem very shaky on this material — do you have a teacher you can ask for some help? If not, the Khan Academy videos have been very good, in my experience. https://www.khanacademy.org/math/algebra/exponent-equations/simplifying-radical-expressions/v/radical-equivalent-to-rational-exponents-2