Question

If the area of a trapezoid is 104 cm squared , a = 4x -1 cm, b = x+2 cm , and h = 8 cm , calculate the length of the longer base

Answer 1

we are given trapezoid

Area is 104cm^2

a=4x-1 cm

b=x+2 cm

h=8cm

we can use area formula

$Area=\frac{1}{2} (a+b)*h$

we can plug above values

$104=\frac{1}{2} (4x-1+x+2)*8$

now, we can solve for x

$104=\frac{1}{2} (5x+1)*8$

$13=\frac{1}{2} (5x+1)$

$26= (5x+1)$

$5x=25$

so, we get

$x=5$

length of longer base is a

we can plug x=5 into a

$a=4*5-1$

$a=19cm$...............Answer

Answer 2

The formula of an area of a trapezoid:

$A=\dfrac{a+b}{2}\cdot h$

We have:

$a=4x-1;\ b=x+2;\ h=8;\ A=104cm^2$

Substitute:

$\dfrac{4x-1+x+2}{2}\cdot8=104\\\\\dfrac{5x+1}{1}\cdot4=104\ \ \ |:4\\\\5x+1=26\ \ \ |-1\\\\5x=25\ \ \ |:5\\\\x=5$

The longer base is a = 4x - 1.

Substitute the value of x to the equation:

$a=4(5)-1=20-1=19$

Answer: 19 cm.