MHB Distance Across I Don't Know Where to Begin

  • Thread starter Thread starter Ilikebugs
  • Start date Start date
AI Thread Summary
The discussion revolves around determining the dimensions of a white rectangle within a tile, defined by segments with one and two tick marks, represented as lengths $a$ and $b$. The relationship between these lengths is established with the equation $a^2 + b^2 = 50$. Using the Pythagorean theorem, the diagonal length of the rectangle, denoted as $\overline{MK}$, is calculated as $\sqrt{2(a^2 + b^2)}$. Substituting the known value, the final length of $\overline{MK}$ is determined to be 10 cm. The conversation effectively concludes with the confirmation of this diagonal length.
Ilikebugs
Messages
94
Reaction score
0
View attachment 6484 I don't know where to begin
 

Attachments

  • potw 3.png
    potw 3.png
    13.4 KB · Views: 110
Mathematics news on Phys.org
I would let $a$ be the length (in cm) of the segments with 1 tick mark, and $b$ be the length (in cm) of the segments with 2 tick marks. And so, given the statement regarding the area of the colored sections, we may write:

$$a^2+b^2=50$$

In terms of $a$ and $b$, what are the dimensions of the white rectangle within the tile?
 
√2a^2 and √2b^2
 
Ilikebugs said:
√2a^2 and √2b^2

Not quite...it would be $$\sqrt{2}a$$ and $$\sqrt{2}b$$...so what would the diagonal of the rectangle be?
 
sqr(2a+2b) ?
 
Ilikebugs said:
sqr(2a+2b) ?

Using the Pythagorean theorem, we find:

$$\overline{MK}=\sqrt{(\sqrt{2}a)^2+(\sqrt{2}b)^2}=\sqrt{2\left(a^2+b^2\right)}$$

Now, we know that $a^2+b^2=50$, so what is the length of $\overline{MK}$?
 
|MK|=√(a√2)^2+(b√2)^2?
 
Ilikebugs said:
|MK|=√(a√2)^2+(b√2)^2?
MK equals 100?
 
Ilikebugs said:
MK equals 100?

$$\overline{MK}=\sqrt{(\sqrt{2}a)^2+(\sqrt{2}b)^2}=\sqrt{2\left(a^2+b^2\right)}=\sqrt{2(50)}=\sqrt{100}=10$$ :D
 

Similar threads

Replies
2
Views
1K
Replies
3
Views
1K
Replies
5
Views
2K
Replies
3
Views
2K
Replies
15
Views
2K
Replies
2
Views
2K
Back
Top