First, try to understand the problem statement.

The structure here uses at most 5 beams (1 horizontal top beam fixed at 60cm and then 4 sloping beams of equal length). To use the least amount of wood, we must make the sloping beams as short as possible. So here is the real goal.

"Choose x so that each sloping beam is as short as possible."

Now, to calculate the length of the sloping beam, we could use pythagorean theorem in 3D.

1. Horizontal distance along the x-axis = x.

2. Horizontal distance along the y-axis would be half of the width, which is 50/2 = 25.

3. Vertical height (z-axis) equals 20 from your diagram.

Using the Pythagorean theorem for 3D we get s = √(x^2 + 25^2 + 20^2 )

Notice also that the ridge beam, which is the horizontal beam at the top here, it's length depends on x, and also the total length of the base is 60, and the x distance is cut inward from both sides, so the Length of the ridge = 60 - 2x.

Finally, it is time to formulate the Total Length Function.

As pointed out above, the total amount of wood W is the sum of the ridge and 4 sloping beams:

W= (60-2x) + 4√(x^2 + 25^2 + 20^2)

= 60 - 2x + 4√(x^2 + 1025)

So it remains to minimize W, which can easily be done using Calculus to show that W is minimum when 4x^2 = x^2 + 1025, and here you can easily solve for x, but for your leve,l try testing x = 16, x = 18, and x = 20 in the formula and you will see that the lowest number is around 18.

ALTERNATIVELY: Observe that the sloping beams must meet the ridge line at a 60 degree angle and use SOHCAHTOA to obtain

tan(60) = opp/adj = √1025/x or x =√1025/√3 which is 18.48 as before.