A right isosceles triangle has side lengths of 13.2, 13.2, and 18.6 meters. What is the hypotenuse of a similar triangle with legs 4.4 meters in length
In a right isosceles triangle, the two legs are congruent. So, if the sides of the right isosceles triangle are 13.2 meters, the length of the hypotenuse can be found using the Pythagorean theorem:
\(c^2 = a^2 + b^2\)
\(c^2 = 13.2^2 + 13.2^2\)
\(c^2 = 174.24 + 174.24\)
\(c^2 = 348.48\)
\(c = \sqrt{348.48} \approx 18.65\)
Therefore, the length of the hypotenuse is approximately 18.65 meters.
Now, to find the hypotenuse of the similar triangle with legs of 4.4 meters, we can set up a proportion:
\(\frac{4.4}{13.2} = \frac{h}{18.65}\)
Rearranging, we get:
\(h = \frac{4.4 \times 18.65}{13.2} \approx 6.24\)
Therefore, the hypotenuse of the similar triangle with legs of 4.4 meters is approximately 6.24 meters.