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# trapezoid geometry problem!

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The bases of an isosceles trapezoid have lengths that differ by 30. The two legs of the trapezoid
have length 25, and the two diagonals of the trapezoid have length 52. What is the area of the
trapezoid?

so far, I've figured out that the trapezoid's area is 20x + 300 (where x is the shorter base) but i don't know how to figure out what x is...

Jun 26, 2020

#1
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From the right triangle with hypotenuse 25 and base 15, we know the height of the trapezoid is 20, by the Pythagorean Theorem.

Another right triangle is with hypotenuse 52, height 20, and base x+15.

So (x+15)^2+400=52^2

This simplifies to x^2+30x-2079=0

Factorizing, we get (x-33)(x+63).

Since x=-63 makes the area negative, x=33.

Jun 26, 2020
edited by thelizzybeth  Jun 26, 2020
edited by thelizzybeth  Jun 26, 2020
#3
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ohhh tysm for the great explanation!!! :)

#2
+1361
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The bases of an isosceles trapezoid have lengths that differ by 30. The two legs of the trapezoid
have length 25, and the two diagonals of the trapezoid have length 52. What is the area of the
trapezoid?

Jun 27, 2020
#4
+732
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wow great picture! thank you!