Sunday, July 30, 2023

figure it out

Another ridiculously easy one:

My answer will be in the comments.



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Posted by Kevin Kim at 7/30/2023 10:41:00 PM

1 comment:

Kevin Kim said...

There's very little actual math to do in this one. You just need to reason some things out.

First, remember that a trapezoid's area is the average of its top and bottom lengths times its height.

We're given a height of 2x - 3.

The top side's length is x + 3.

The bottom side's length 3x - 1.

There's a segment going through the middle of the trapezoid that's got a length of 15. We know it's going through the middle because we see congruency lines on both sides. So the segment is parallel to the top and bottom.

This means we know that 15 is the average of the top and bottom sides. The math's basically been done for us. All we have to do is solve for x by averaging out (x + 3) and (3x - 1) and equating that average to 15.

So:

[(x + 3) + (3x - 1)] / 2 = 15

(4x + 2) / 2 = 15

4x + 2 = 30

2x + 1 = 15

2x = 14

x = 7.

All we need to do now is plug 7 into the formula for the trapezoid's height:

2(7) - 3 = 11 = h

We already know the average of the top and bottom—15—so we multiply 15 times the height of 11, and:

15•11 = 165.

So: 165 is the trapezoid's area.

QED. And with relatively little math.

July 30, 2023 at 10:52:00 PM GMT+9

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