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 cm2 , find the length of the larger base.

Answer 1

Answer:

Length of the larger base is 19 cm.

Step-by-step explanation:

Height of the trapezoid = (x - 4)

Bases of the trapezoid = (x + 4) and (x + 9)

Area of the trapezoid = 99 cm²

We know the formula,

Area of trapezoid = $\frac{1}{2}(\text{Sum of bases})\times (\text{Distance between the bases}})$

99 = $\frac{1}{2}[(x + 4)+(x + 9)](x - 4)$

99 = $\frac{1}{2}[2x + 13](x - 4)$  

99×2 = (2x + 13)(x - 4)

198 = 2x² - 8x + 13x - 52

2x² + 5x - 52 - 198 = 0

2x² + 5x - 250 = 0

2x² + 25x - 20x - 250 = 0

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

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

(2x + 25) = 0

2x = -25

x = -$\frac{25}{2}$

Since length of the base can not be negative.

Therefore, (x - 10) = 0 will be the solution

x = 10 cm

Length of the larger base = x + 9

= 10 + 9

= 19 cm

Answer 2

Answer: 19 cm

Step-by-step explanation:

$A_{trapezoid}=\frac{b_{1}+b_{2}}{2}*h$

                99 = $\frac{(x+4 + x+9}{2}*(x - 4)$

                99 = $\frac{(2x + 13}{2}*(x - 4)$

              198 = (2x + 13)(x - 4)

              198 = 2x² + 5x - 52

                 0 = 2x² + 5x - 250

                 0 = 2x²- 20x + 25x - 250

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

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

0 = 2x + 25     or        0 = x - 10

  $-\frac{25}{2}$ = x      or          x = 10

Since length cannot be negative, $-\frac{25}{2}$ can be disregarded

Larger base: x + 9  = 10 + 9   = 19