Calculate the base of the rectangle?

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Answer 1 · 2016-04-25T09:40:06

$bar(AD)=500"cm"$

The shaded area is the difference between the area of the rectangle and the area of the triangle.

The area of the rectangle is given by the product of the side lengths

$A_"rect"=800x$

The area of the triangle is given by half the product of the base and the height, which match the lengths of the rectangle.

$A_"tri" = 1/2(800x)=400x$

Using the given value for the shaded area, that gives us

$200000 = 800x-400x = 400x$

$=> x = 200000/400 = 500$

And so the base $bar(AD)$ is $500"cm"$