smc

Question

A thin piece of wood of uniform density in the shape of an equilateral triangle with side length 3 inches weighs 12 ounces. A second piece of the same type of wood, with the same thickness, also in the shape of an equilateral triangle, has side length of 5 inches. Which of the following is closest to the weight, in ounces, of the second piece?

Accepted Answer

We can solve this problem by using similar triangles, since two equilateral triangles are always similar. We can then use (35)^2=12x. We can then solve the equation to get x=1003 which is closest to 33.3 Sidenote - If we didn't know that (ab)^2 for an equilateral triangle, using the area formula, 143a^2, in proportion 1/4(3a^2)1/4(3b^2), just cancel and simplify to get a^2b^2.