About how many feet of fencing are needed to enclose a rectangular garden with a 30 foot pond side and a 40 foot long diagonal

Hello there!

If you want to enclose a rectangular garden, then the feet of fencing that you need are equal to the perimeter of the rectangle, this is, the sum of all the sides of the rectangle.

We know that the rectangle has a 30ft pond side and a 40ft long diagonal.

this 40ft diagonal is the hypotenuse of a triangle rectangle where the cathetus is the sides of the rectangle; we know that one of the sides are of 30 ft, and we want to find the other:

Using the Pythagorean theorem; we know that:

where x is the length of the other side that we don't know yet.

Then your rectangle has a 30ft side, and a 26.5ft side (and has two of both)

Then the perimeter is:

30ft + 30ft + 26.5ft + 26.5ft = 113ft

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.