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 99 cm^2 Find the length if t

Question

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 99 cm^2 Find the length if the larger base 

Answer 1

Area = 1/2(height)( base1 + base2)

99 = 1/2(x-4)( x+4 + x+9)

99 = 1/2(x-4)(2x + 13)

198 = (x-4)(2x + 13)

198 = 2x^2 + 13x - 8x - 52

0 = 2x^2 + 5x - 250

0 = (2x + 25 )(x - 10 )

2x + 25 = 0 ---> x = -25/2 ---> x-4 < 0 and the height cannot be negative.

x - 10 = 0 ---> x = 10

Height is 6, legs are 14 and 19

1/2*6*(14 + 19) = 3 x 33 = 99

Answer 2

Area = (1/2)(base 1 + base 2)(height)

 

2Area = height(base 1 + base 2)

 

2(99) = (x - 4)(x + 4 + x + 9)

 

198 = (x - 4)(2x + 13)

 

198 = 2x² + 5x - 52

 

 

Subtract 198 to both sides of the equation.

 

0 = 2x² + 5x - 250

 

 

Factor by grouping.

 

0 = 2x² + 25x - 20x - 250

 

0 = 2x² - 20x + 25x - 250

 

0 = 2x(x - 10) + 25(x - 10)

 

0 = (2x + 25)(x - 10)

 

Setting these factors equal to zero, we get  x=10  and x=-12.5

 

 

We accept the positive x value.

 

Your larger base is (x + 9).  Therefore, your larger base is 10cm.