Question

Can anybody help me with this word problem?

A homeowner, who loves math, decides to make a garden/patio area in the following way. She decides to make the gardening area, where she will plant roses bushes in the shape of an equilateral triangle having a side length of 10 feet. She then constructs 3 isosceles triangle concrete pads, so that their bases are on the sides of the equilateral triangle. She constructs them so that the sum of the area of the three isosceles triangles is equal to the area of the equilateral triangle. What are the dimensions of the isosceles triangle? Please give an exact answer (Like √2 instead of 1.4142135)

Answer 1

The equilateral triangle has area 25√3

So, now we have 3 isosceles triangle, each of area 5h, which add up to 25√3.

Each concrete triangle thus has area 25/√3, so their height is

5h = 25/√3
h = 5/√3

Answer 2

A square has side length 6.04x10^-5meters. What is the area?