Final answer:
To find the total length of fencing Latasha needs to purchase for her triangle-shaped garden, we can calculate the perimeter by adding up the lengths of all three sides. By applying the Pythagorean theorem, we can find the length of the third side of the triangle. Adding up the lengths of all three sides gives us the total length of fencing Latasha needs to purchase.
Step-by-step explanation:
To find the total length of fencing Latasha needs to purchase, we need to calculate the perimeter of her garden. Since her garden is shaped like a triangle, we can add up the lengths of all three sides.
Given that the first side is 80.0 m long and the next side is 105 m long, we can find the length of the third side using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's call the length of the third side C. We can use the formula C = sqrt(A^2 + B^2), where A is the length of the first side (80.0 m) and B is the length of the second side (105 m).
Plugging in the values, we have C = sqrt(80.0^2 + 105^2) = sqrt(6400 + 11025) = sqrt(17425) = 131.98 m (rounded to two decimal places).
Now we can calculate the total length of fencing by adding up the lengths of all three sides: 80.0 m + 105 m + 131.98 m = 316.98 m (rounded to two decimal places).