Question

In your town, there is a field that is in the shape of a right triangle with the dimensions shown. (Round answers to the nearest whole number).

The picture is a right triangle with 35 ft as the short side, x ft is the long side, and 80ft is the length of the hypotenuse.

a. Find the perimeter of the field.

About ____ feet.

b. You are going to plant dogwood seedlings about every ten feet around the field's edge. How many trees do you need?

About______trees.

c. If each dogwood seedling sells for $12, how much will the trees cost?

About______ dollars

How would you do problems a and b step by step?

Answer 1

a. To find the perimeter of a right triangle, use the Pythagorean theorem to find the length of the missing side, then add the lengths of all three sides. b. To find the number of trees needed, calculate the number of intervals of 10 feet that can fit along the perimeter of the field.

Step-by-step explanation:

a. Find the perimeter of the field:

To find the perimeter of a triangle, you add the lengths of all three sides. Since the field is in the shape of a right triangle, we can use the Pythagorean theorem to find the length of the missing side. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, we have a = 35 ft and c = 80 ft. Using the formula, we can solve for b: b = sqrt(c^2 - a^2). Plugging in the values, we have b = sqrt(80^2 - 35^2) = sqrt(6400 - 1225) = sqrt(5175) ≈ 71.94 ft.

Now, we can find the perimeter by adding all three sides: perimeter = a + b + c = 35 ft + 71.94 ft + 80 ft ≈ 186 ft. Therefore, the perimeter of the field is about 186 feet.

b. You are going to plant dogwood seedlings around the field's edge:

To find the number of trees needed, we need to calculate the number of intervals of 10 feet that can fit along the perimeter of the field. The perimeter of the field is 186 feet, so we divide it by 10 to get the number of intervals: intervals = 186 ft / 10 ft = 18.6 intervals. Since we can't have a fraction of an interval, we round up to the nearest whole number, which gives us the number of trees needed: trees = ceil(18.6) ≈ 19 trees.

Answer 2

a. about 187 feet

b. about 19 trees

c. about 228 dollars

What we know:

• 80 ft = hypotenuse
• 35 ft = short side
• x ft = long side
• it is a right triangle

a. Find the perimeter of the field. about 187 feet

solve for the missing side length ('x'):

1. 35^2 + x^2 = 80^2
2. 1225 + x^2 = 6400
3. x^2 = 5175
4. x = 15sqrt(23) or approx. 71.92

add all side lengths:

1. P = 80 + 35 + 71.92
2. P = 115 + 72 (rounded)
3. P = 187 ft

b. You are going to plant dogwood seedlings about every ten feet around the field's edge. How many trees do you need? about 19 trees

1. divide perimeter by 10 187/10 = 18.7
2. round 18.7 trees = about 19 trees

c. If each dogwood seedling sells for $12, how much will the trees cost? about $228

1. multiply trees by cost of each $12 x 19 trees = $228
2. about $228 for the trees