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)

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

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

Sure, I'd be happy to help you with this word problem!

To solve this problem, we need to find the dimensions of the isosceles triangles such that the sum of their areas is equal to the area of the equilateral triangle.

First, let's calculate the area of the equilateral triangle. The formula to find the area of an equilateral triangle is A = (√3/4) * s^2, where A is the area and s is the length of one side.

In this case, the side length of the equilateral triangle is given as 10 feet, so we can substitute this value into the formula:

A = (√3/4) * (10)^2
A = (√3/4) * 100
A = (√3/4) * 100
A = (√3) * 25
A = 25√3

So the area of the equilateral triangle is 25√3 square feet.

Now, let's find the dimensions of the isosceles triangles, which we'll denote as b (base) and h (height).

Since the isosceles triangles have their bases on the sides of the equilateral triangle, the base of each isosceles triangle will be equal to one side length of the equilateral triangle, which is 10 feet.

To find the height (h) of the isosceles triangle, we can use the formula for the area of a triangle, which is A = (1/2) * b * h.

Since we know that the sum of the areas of the three isosceles triangles is equal to the area of the equilateral triangle, we can set up the equation:

(1/2) * b * h + (1/2) * b * h + (1/2) * b * h = 25√3

Simplifying the equation, we have:

(3/2) * b * h = 25√3

To isolate h, we divide both sides of the equation by (3/2) * b:

h = (25√3) / ((3/2) * b)

Now, we can substitute the value of b as 10 feet:

h = (25√3) / ((3/2) * 10)
h = (25√3) / (30/2)
h = (25√3) / 15
h = (5√3) / 3

So the height (h) of each isosceles triangle is (5√3) / 3 feet, and the base (b) is 10 feet.

Therefore, the dimensions of the isosceles triangle are a base length of 10 feet and a height of (5√3) / 3 feet.