the question is posted below with an explanation of the matching image

Question

Two neighbouring houses are located at A and B, near a straight section of a rural road, RD. The electric company plans to place a pole P, at the roadside and connect wires from the pole to the two houses. How far from point R should the pole be located so that the minimum length of wire is needed?

The answer is 30 I believe, but can you should me how to get the answer?

 it doesnt let me post it as an image but I can explain the image. So there are two triangles, both right angles triangle one is on the left and has point A at the top, point R at the bottom and point P in the middle. From point A to R, we have 30 m Triangle 2 has point B at the top, point D at the bottom to right and point p in the middle. From point B to D, we have 60m. And from point R to P to D, we have 90 m

Answer 1

This is a question that is fairly straight forward in Calculus but not so much trying to use Algebra. If I were forced to stick with Algebra, I would write the equation and use a graphing calculator to find the minimum point.

I'm assuming the sketch looks like this:

except that I've added "x" and "90 - x" as well as d₁ and d₂.. Use the Pythagorean Theorem to solve for the length of the hypotenuse of both triangles (d₁ and d₂):

Left triangle: d₁ = √(30² + x²)

Right triangle: d₂ = √((90 - x)² + 60²)

Total distance to be minimized is d₁ + d₂:

d(x) = √(30² + x²) + √((90 - x)² + 60²)

d(x) = √(900 + x²) + √(8100 - 180x + x²) + 3600)

d(x) = √(900 + x²) + √(x² 180x + 11700)

If you graph this function in desmos or on your TI-84 calculator you'll see the minimum value occurs at x = 30.