Triangle Dimensions: One leg of a right triangle is 10cm....

[silverdragon316]

Triangle Dimensions. One leg of a right triangle is 10cm. The other sides have legnths that are consecutive even integers. Find the lengths.

Would the problem begin like this?

10^2+x^2=(x+2)^2

100+x^2=x^2+4x4

98=4x

24=x

If this is correct what is my next step?

 

[tkhunny]

You should ask, "What is my FIRST step?" The answer to this will help you with your last step.

WRITE DOWN a clear definition.

x = The first of the two consecutive even integers.

x+2 = The second of the two consecutive even integers.

Note: There really is nothing in this definition that forces the result to produce an EVEN integer. If you get something else, you'll have to write a better definition.

 

[stapel]

Re: Triangle Dimensions: One leg of a right triangle is 10cm

10^2+x^2=(x+2)^2

100+x^2=x^2+4x4x

You might want to check your multiplication: (x + 2)(x + 2) does not equal x² + (4x)².

Your initial set-up is correct, by the way.

Eliz.

 

[soroban]

Re: Triangle Dimensions: One leg of a right triangle is 10cm

Hello, silverdragon316!

One leg of a right triangle is 10cm.
The other sides have legnths that are consecutive even integers.
Find the lengths.

Would the problem begin like this?

. . \(\displaystyle 10^2\,+\,x^2\:=\x\,+\,2)^2\;\;\) Yes!

. . \(\displaystyle 100\,+\,x^2\:=\:x^2\,+\,4x\,+\,4\)

. . \(\displaystyle \not{98}\:=\:4x\;\;\) no: 100 - 4 = 96

. . \(\displaystyle \not{24}\:=\:x\;\;\) no: 98 ÷ 4 = 17

If this is correct, what is my next step?

Answer the question: "Find the lengths".

We have: \(\displaystyle \:4x\:=\:96\;\;\Rightarrow\;\;x\:=\:24\)

We have: one leg is \(\displaystyle \fbox{10}\) cm.
We found that another leg is: \(\displaystyle x\,=\,\fbox{24}\)
Then the other side is: \(\displaystyle x\,+\,2\:=\:\fbox{26}\)

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Check

Does: \(\displaystyle 10^2\,+\,24^2\:=\:26^2\) ? . . . Yes!