Question

a garden has the shape of a right-angled triangle with sides of length 30, 40 and 50. a straight fence goes from the corner with the right-angle to a point on the opposite side, dividing the garden into two sections which have the same perimeter. how long is the fence?

Answer 1

To find the length of the fence, use the Pythagorean theorem to determine the length of the third side of the triangle. Divide the perimeter of the garden in half and subtract the lengths of the other two sides to find the length of the fence. The length of the fence is 10 units.

Step-by-step explanation:

To find the length of the fence, we need to determine the length of the third side of the triangle created by the garden. Using the Pythagorean theorem, we can determine that the third side is 50 units long. Since the perimeter of each section of the garden is the same, we can divide the perimeter of the garden in half and subtract the lengths of the other two sides to find the length of the fence.

First, we find the perimeter of the garden by adding the lengths of all three sides: 30 + 40 + 50 = 120.

Next, we divide the perimeter in half: 120/2 = 60.

Then, we subtract the lengths of the other two sides: 60 - 30 - 40 = 60 - 70 = -10.

Finally, we take the absolute value of the result to get the length of the fence: |-10| = 10.

Therefore, the length of the fence is 10 units.

Answer 2

To divide the garden into two sections with the same perimeter, the length of the fence would be 70 units.

Step-by-step explanation:

To solve this problem, we need to find the length of the fence that divides the garden into two sections with equal perimeter.

First, let's find the perimeter of the entire garden. The perimeter of a triangle is the sum of its sides. In this case, the perimeter is 30+40+50 = 120 units.

Since we want to divide the garden into two equal sections, each section will have a perimeter of 120/2 = 60 units.

Now, let's find the length of the fence. Let's assume that the fence starts at the corner with the right-angle and goes to a point on the opposite side (the hypotenuse).

Since the two sections have equal perimeter, the sum of the other two sides of the triangle (excluding the hypotenuse) should be equal to the length of the fence. In this case, the sum of the other two sides is 30+40 = 70 units, which is the length of the fence.