# Solve this geometry problem

I have a problem I made but I can't solve it. If the problem doesn't have enough information to be solved, please explain why below.

Here's the problem: You have two semicircles of radius 1 on top of an isosceles triangle of base and height 4, making a heart shape.

You make two lines, as shown, that divides the heart into three shapes of equal area. What is the length of each of these lines?

Note by Mr.Person 12345
1 year ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

Consider that the central area is a kite, which has area pq/2, where p and q are the diagonals. The area of this kite is given by one third the area of the shape, (pi+8)/3. Also consider that the lower triangle created by drawing the horizontal diagonal is similar to the original isosceles triangle. You should be able to find the legs of the right triangles formed by the diagonals, for which x is the hypotenuse, and find the length to be approximately 2.33555.

- 8 months, 3 weeks ago

Thank you!

- 8 months, 3 weeks ago