Final answer:
The length of the hypotenuse can be found using the Pythagorean theorem. In this case, the length of the other side, labeled 'b', can be found using the given area of the triangle. Substituting this value into the equation, we can find the length of the hypotenuse.
Step-by-step explanation:
The length of the hypotenuse can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the two sides are 10 ft and the unknown length of the hypotenuse. So, we have:
a² + b² = c²
10² + b² = c²
100 + b² = c²
To find the length of the hypotenuse, we need to know the length of the other side, labeled 'b'. The area of the triangle is given as 200 ft², which can be used to find the length of 'b'. The area of a triangle is equal to 1/2 the product of the base and height, so:
1/2 * 10 * b = 200
5b = 200
b = 200/5 = 40
Now, we can substitute this value of 'b' into the equation to find the length of the hypotenuse:
100 + 40² = c²
100 + 1600 = c²
1700 = c²
c = √1700 ≈ 41.2
Therefore, the length of the hypotenuse is approximately 41.2 ft, rounded to the tenths place.