Sides of square increased by 1/3

[GWW]

If sides of square s are increased by 1/3, what is length of new diagonal?
New sides are now 4/3s. Using Pythagorean theory 4/3s^2 + 4/3s^2 = c^2
How do we get to final answer of
C = 4s times sq root of 2 all divided by 3. (Sorry not sure how to type in sq root symbol

 

[Otis]

… 4/3s^2 + 4/3s^2 = c^2 … How do we get to final answer of
C = 4s times sq root of 2 all divided by 3 …

Hello GWW. You need to type grouping symbols around expressions that are squared. (Without them above, only the s is squared.)

(4/3·s)^2 + (4/3·s)^2 = c^2

Combine like-terms, on the left-hand side.

(2)(4/3·s)^2 = c^2

Take the square root of each side, and ignore the negative roots.

sqrt(2)·(4/3·s) = c

To rearrange that result as "4s times sq root of 2 all divided by 3", we write √2 and s in rational form before multiplying and then use the commutative property of multiplication to change the order of factors shown in the numerator.

\(\displaystyle \frac{\sqrt{2}}{1} \cdot \frac{4}{3} \cdot \frac{s}{1}\)

\(\displaystyle \frac{\sqrt{2}·4·s}{1·3·1}\)

\(\displaystyle \frac{4s \sqrt{2}}{3}\)

?

 

[GWW]

Thank you!