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Trapezoid Properties - Problem 3
Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
Recall that an isosceles trapezoid has two congruent sides and two parallel sides. Since two of the sides are congruent, their lengths are equal.
When the side lengths are given in terms of a variable, add up these expressions, remembering that the congruent sides are the same length (so if one of the congruent sides is given with length y, the other also has length y). Then, set this equal to the given perimeter, since the perimeter is the sum of the length of all sides of a polygon. Solve for the variable using techniques from algebra.
We can solve for missing side lengths using a little bit of algebra in geometry.
So if you look at this trapezoid I see that I have one pair of congruent sides and another a pair of parallel sides which tells me that this must be a trapezoid. If these two sides are congruent and I’m looking for the perimeter is 46cm, I’m going to label this as 2y. So remember capital P in geometry means perimeter capital A means area.
So if I add up my four sides, which is a definition of my perimeter I get 46cm. So I’m going to write an algebraic equation. 46 is equal to 2y which is one of my sides, plus y plus 10 plus 2y plus my fourth side which is y.
Again my objective here is solving for y. So 46 is equal to if I combine like terms 2 plus 1y is 3, plus 2 plus 1 is 6. So you’ve got a total of 6y's here, plus you’ve got 10 and it doesn’t like any other like terms of 10.
So now I’m going to solve for y by subtracting 10 from both sides. 46 minus 10 is 36 which equals 6y and it's pretty clear that we are going to get y equals 6.
So the key to this problem is remembering that isosceles trapezoids mean that these two legs are going to be congruent to each other and the perimeter means the sum of all the sides of your polygon.
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