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lora16 [44]
2 years ago
15

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

Mathematics
2 answers:
leva [86]2 years ago
8 0

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.

rosijanka [135]2 years ago
5 0

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

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