we are given trapezoid
Area is 104cm^2
a=4x-1 cm
b=x+2 cm
h=8cm
we can use area formula
[tex] Area=\frac{1}{2} (a+b)*h [/tex]
we can plug above values
[tex] 104=\frac{1}{2} (4x-1+x+2)*8 [/tex]
now, we can solve for x
[tex] 104=\frac{1}{2} (5x+1)*8 [/tex]
[tex] 13=\frac{1}{2} (5x+1) [/tex]
[tex] 26= (5x+1) [/tex]
[tex] 5x=25 [/tex]
so, we get
[tex] x=5 [/tex]
length of longer base is a
we can plug x=5 into a
[tex] a=4*5-1 [/tex]
[tex] a=19cm [/tex]...............Answer
The formula of an area of a trapezoid:
[tex]A=\dfrac{a+b}{2}\cdot h[/tex]
We have:
[tex]a=4x-1;\ b=x+2;\ h=8;\ A=104cm^2[/tex]
Substitute:
[tex]\dfrac{4x-1+x+2}{2}\cdot8=104\\\\\dfrac{5x+1}{1}\cdot4=104\ \ \ |:4\\\\5x+1=26\ \ \ |-1\\\\5x=25\ \ \ |:5\\\\x=5[/tex]
The longer base is a = 4x - 1.
Substitute the value of x to the equation:
[tex]a=4(5)-1=20-1=19[/tex]
Answer: 19 cm.
