Three 2 x 1 rectangles are arranged as shown. What fraction of the figure is golden?

Guest Nov 18, 2019

#1**0 **

It might be 1/5??

because i'm assuming that the two golden parts on the overlapping triangle equal 1/2 of the overlapping triangle

because the golden parts overlap, the area is not counted twice so therefore there would be 5 halves and since the two golden triangles make one half of the rectangle(that's an assumption!!) so it would be one out of five halves are golden

once agaain i am very unsure of whether that logic is reasonable or not but i believe it's somewhat correct

htzhang919 Nov 19, 2019

#4**0 **

just curious, why did you delete all your questions and answers? i found this after checking your profile...

CalculatorUser
Nov 19, 2019

#2**+2 **

This is a fun problem! Here is the pic:

Notice the **red **and **green** triangles. The red triangle has a base of 1 and a width of 2, based on Pytahgorean theorem, we can conclude it has a hypotenuse of \(\sqrt{5}\).

**Notice how the red and the green triangles SHARE a hypotenuse.**

We know that one of the legs of the green triangle has a length of 2. The red and green triangle share a hypotenuse, so knowing the green triangle's hypotenuse and one of its legs, we can conclude through the pythathoream theorem that the base of the triangle is 1.

With this information, the red and the green triangle have EQUAL areas.

We know the area of the RED triangle from the previous picture is 2 * 1 = 2/2 = **1**.

Can you solve this? I know I can't. Help.

CalculatorUser Nov 19, 2019

#5**0 **

I got it answered on stack exchange -> https://math.stackexchange.com/questions/3442907/rectangular-figure-with-unknown-area-and-possibly-similar-triangles/3442923#3442923

CalculatorUser Nov 20, 2019