Question

Find the diameter of the largest circular pond that could fit in a triangular garden with vertices at (18,54), (-27,36), & (27,-18), where a unit represents 1m.

Answer 1

Answer: The diameter of the largest circular pond that could fit in a triangular garden with vertices at (18,54), (-27,36), & (27,-18) is 34.5m.

Step-by-step explanation:

Let the vertices of the triangle are A(18,54), B(-27,36), & C(27,-18).

Use distance formula to find the length of sides.

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using the above formula the distance between AB is 48.5, BC is 76.4 and AC is 72.6.

The length of sides are 48.5, 76.4 and 72.6.

Formula to find semi-perimeter is given below,

`s=(a+b+c)/(2)`

Where a, b and c are the length of sides.

`s=(48.5+76.4+72.6)/(2)`

`s=98.75`

The formula to find the radius of the circle pond in the triangle is given below,

`r=\sqrt{((s-a)(s-b)(s-c))/(s)}`

`r=\sqrt{((98.75-76.4)(98.75-72.6)(98.75-48.5))/(98.75) }`

`r=√(297.4)`

`r=17.25`

The radius of the circle is 17.25 m.

`D=2r`

`D=2(17.25)`

`D=34.5`

Therefore, the diameter of circle is 34.5 m.