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

The formula of an area of a trapezoid:

`A=(a+b)/(2)\cdot h`

We have:

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

Substitute:

`(4x-1+x+2)/(2)\cdot8=104\\\\(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.

Answer 2

we are given trapezoid

Area is 104cm^2

a=4x-1 cm

b=x+2 cm

h=8cm

we can use area formula

`Area=(1)/(2) (a+b)*h`

we can plug above values

`104=(1)/(2) (4x-1+x+2)*8`

now, we can solve for x

`104=(1)/(2) (5x+1)*8`

`13=(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