The height of a trapezoid can be expressed as x-4, while the bases can be expressed as x+4 and x+9. if the area of the trapezoid is 99cm^2, find the length of the larger base?

Check the picture below.

keeping in mind that "x" cannot be equal to -25, since that'd give us negative values on either base and the bases are a positive value.

  19 cm

Step-by-step explanation:

Since we want to find the length of the longer base, let that be represented by z. Then we have ...

  z = x+9

  x = z-9

The other dimensions of the trapezoid are then ...

  shorter base = x +4 = (z -9) +4 = z -5

  height = x -4 = (z -9) -4 = z -13

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The formula for the area of a trapezoid is ...

  A = (1/2)(b1 + b2)h = (1/2)(z +(z -5))(z -13) = (1/2)(2z -5)(z -13)

The area is 99 cm², so we have ...

  99 = 1/2(2z² -31z +65)

  2z² -31z -133 = 0 . . . . multiply by 2 and subtract 198

  (2z +7)(z -19) = 0 . . . . factor

This has one positive solution: z = 19

The length of the larger base is 19 cm.

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step-by-step explanation: