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3 June, 19:38

The height of a trapezoid is 8 inches and it's area is 96 inches. One base of the trapezoids is 6 inches longer than the other base. What are the lengths of the bases? Explain how you found your answer

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  1. 3 June, 20:50
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    There is a common equation we use to find the Area of a trapezoid.

    (a+b) h/2=A

    Let's fill in what we know. We're not going to fill in any information about the bases.

    (a+b) 8/2=96

    We can already tell that 8/2 will simplify to 4.

    (a+b) 4=96

    Let's divide each side by 4.

    a+b=24

    Now, let's look at the information about the bases.

    So, we will have this in terms of base a, since one base is longer than the other. This is how it'll look.

    a + (a+6) = 24

    We can simplify that further.

    2a+6=24

    now subtract 6 from each side.

    2a=18

    Let's divide

    9=a

    So one side is 9, so the other one is 15. We should make sure everything makes sense by putting all the information in the formula to find area.

    (9+15) 8/2

    24*4

    96.

    The lengths of the bases are 9 and 15 inches.
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