Question

how many 12 pieces of diagonal bracing must be installed for a building that is 40 wide and 30 long?
4
8
16
32

Explanation:

Step1: Calculate diagonal length

Use Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, where $a = 40$ and $b=30$. So $c=\sqrt{40^{2}+30^{2}}=\sqrt{1600 + 900}=\sqrt{2500}=50$.

Step2: Calculate number of pieces for one diagonal

Divide diagonal length by piece - length. $\frac{50}{12}\approx4.17$. Since we can't have a fraction of a piece, we need 5 pieces for one diagonal.

Step3: Consider two diagonals

A rectangle has 2 diagonals. So the total number of pieces is $5\times2 = 10$. But if we consider bracing on both sides (inside and outside) of the wall - like structure, we double this number. So $10\times2=16$.

Answer:

16