## Algebra 1

$2w\sqrt{34}$ yd
The diagonal forms a right triangle. Use the Pythagorean Theorem to find the length from corner to corner. $a^2+b^2=c^2\longrightarrow$ substitute the given values $(6w)^2+(10w)^2=c^2\longrightarrow$ simplify $36w^2+100w^2=c^2\longrightarrow$ add $136w^2=c^2\longrightarrow$ find the square root of each side $\sqrt{136w^2}=\sqrt{c^2}\longrightarrow$ factor out the perfect square $\sqrt{4w^2\times34}=c\longrightarrow$ multiplication property of square roots $\sqrt{4w^2}\times\sqrt{34}=c\longrightarrow$ simplify $2w\sqrt{34}=c$