Geometry Word Problem

If a square has 1m sides and we want to divide it into three segments, two that have the same longitude and are trianlges represented by x.  All three segements have the same area. How much is x?

Note: I don't even know if its possible from the information I gave you, it was translated from spanish and had a picture, if it's not possible to answer with this information please say so.


Expert Answers

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Start by drawing a square with dimensions of 1 x 1. Then, draw a line from the top right hand corner to the base of the square such that the line you're drawing intersects 1/3 of the distance from the bottom left hand corner. Repeat this for the bottom left hand corner so that a line from this corner intersects the top line of the square 1/3 of the distance from the top right hand corner. Lable these two triangles as triangle 1 and triangle 2. Wish I could include a picture, but can't seem to.

The area of triangle 1 and 2 is the equation A = 1/2

2bh. Since the square is 1m X 1m, we know the area of triangle 1 and 2 must each be 1/3 of the total. So, ⅓ = ⅟2bh. We also know h = 1. Therefore, ⅓ = ⅟2b(1). Solving for b, we find b = 2/3. Then we can use the Pythagorean Theorem a^2 + b^2 = c^2. We know a and b, therefore we can solve for c. Let a = 1, b = 2/3. We find c = √(13/9), or c = (√13)/3. In this case c, or what you are calling x, is (√13)/3.

This creates two triangles with a hypotenuse of equal lengths, and 3 shapes with equal area. This is the best I can offer based on the info you provided. Hope it helps.

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