# Finding the sides of a trapedzoid using only Angles and perimeter

Dramen

## Homework Statement

My knowns are: the trapezoid has a perimeter equal to 180 inches
and it's base angles are ∏/3

The unknowns are: the lengths of the base (x) and the length of one of the slanted sides (y)
as well as the relationship between x and y

Trig equations

## The Attempt at a Solution

I pretty much split up the trapezoid into 2 right triangles and a rectangle. The triangle creates a 30-60-90 right triangle giving me the length ratios of the sides. This is where I hit my dead end because I have no idea how to find the lengths of the triangles without a single length of any of the triangle's sides. My friend was able to guess and check the correct lengths of x=75 inches and y=30 inches.

I want to know if it's possible to find any of the unknown sides without having to resort to a guess and check method. Also I'm not sure, when it says to deduce a relationship between x and y if it means to create some sort of formula that relates them or something.

Any insight on this is appreciated and thanks in advance.

Homework Helper
Gold Member

## Homework Statement

My knowns are: the trapezoid has a perimeter equal to 180 inches
and it's base angles are ∏/3

The unknowns are: the lengths of the base (x) and the length of one of the slanted sides (y)
as well as the relationship between x and y

Trig equations

## The Attempt at a Solution

I pretty much split up the trapezoid into 2 right triangles and a rectangle. The triangle creates a 30-60-90 right triangle giving me the length ratios of the sides. This is where I hit my dead end because I have no idea how to find the lengths of the triangles without a single length of any of the triangle's sides. My friend was able to guess and check the correct lengths of x=75 inches and y=30 inches.

I want to know if it's possible to find any of the unknown sides without having to resort to a guess and check method. Also I'm not sure, when it says to deduce a relationship between x and y if it means to create some sort of formula that relates them or something.

Any insight on this is appreciated and thanks in advance.

If you call the base of each of your triangles ##b## don't you see that ##b=y/2##? So you can get the top side in terms of ##x## and ##y##. So with all sides in terms of ##x## and ##y##, write the equation of the perimeter. I think you will find your friends answer is not the only one.

Dramen
I don't completely get your answer, but then it maybe because I'm at fault for poor wording and that my x-value was off. My x=70 had a lapse in thinking for a bit and I may need to clarify what's x and y. The x unknown is the longer base of the trapezoid and the y unknown is the side of the trapezoid.

I broke down the trapezoid into 2 triangles and a single rectangle so that now my y is equal to the triangle's hypotenuse and the x is equal to y + the base of the rectangle on its (rectangle) longer side. The reason x=y + rectangle base is because the short-side of the triangle is equal to the hypotenuse/2 and that 2 would end up being canceled out because there are 2 equal triangles.

I'm sorry if I did not seem as clear, when I first posted my query.

Dramen
Okay getting some time to look at it now I see your point and was able to simplify the expression down to $x = 90 - y/2$

Okay getting some time to look at it now I see your point and was able to simplify the expression down to $x = 90 - y/2$