Question

a snail farmers business is growing. he wants to build a new pen similar to the old one, but with a scale factor of 1:3. this will accommodate the expanding business. the old pen is square. if the diagonal of the old pen measures 10 meters, what is the length of one side of the new pen? use the pythagorean theorem. 21.21 m 7.07 m 100.00 m 50.00 m

Explanation:

Step1: Find side - length of old pen

For a square with diagonal $d$ and side - length $s$, by the Pythagorean Theorem $d^{2}=s^{2}+s^{2}=2s^{2}$. Given $d = 10$ meters, we have $10^{2}=2s^{2}$, so $s^{2}=\frac{100}{2}=50$, and $s=\sqrt{50}=5\sqrt{2}\approx7.07$ meters.

Step2: Find side - length of new pen

The scale factor of the old pen to the new pen is $1:3$. Let the side - length of the old pen be $s_1$ and the side - length of the new pen be $s_2$. Then $\frac{s_1}{s_2}=\frac{1}{3}$. Since $s_1 = 5\sqrt{2}$ meters, $s_2=3\times5\sqrt{2}=15\sqrt{2}\approx21.21$ meters.

Answer:

21.21 m