Figure ABCD is a trapezoid. Find

Mathematics

2 answers:

amid [387]3 years ago

8 0

Answer:

x = 4

Step-by-step explanation:

The mid segment is half the sum of the parallel bases, that is

$\frac{1}{2}$ (2x + 3x + 10) = 15 ( multiply both sides by 2 )

5x + 10 = 30 ( subtract 10 from both sides )

5x = 20 ( divide both sides by 5 )

x = 4

Fittoniya [83]3 years ago

7 0

Answer

Step-by-step explanation:

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A rancher constructs two rectangular horse pastures that share a side, as shown. The pastures are enclosed by 1050 feet of fenci

noname [10]

The complete question in the attached figure

we know that
area each pasture=15000 ft²
area each pasture=x*y
so
15000=x*y-----> equation 1

perimeter two rectangular pastures=1050 ft
perimeter two rectangular pastures=2*[2x+y]+y----> 4x+2y+y---> 4x+3y
so
1050=4x+3y----> divide by 3----> 1050/3=(4/3)x+y
clear variable y
y=350-(4/3)x-----> equation 2

the answer part a)
y=350-(4/3)x------> it was proved

Part b)Find the possible lengths and widths of each pasture.
substitute equation 2 in equation 1
15000=x*y-----> 15000=x*[350-(4/3)x]
15000=350x-(4/3)x²----> multiply by 3----> 45000=1050x-4x²
4x²-1050x+45000=0

using a graph tool----> to resolve the second order equation
see the attached figure

the solution is
x=53.942 ft
x=208.558 ft

15000=x*y-----> y=15000/x

for x=53.94 ft
y=278.09 ft

for x=208.56 ft
y=71.92 ft

the possible lengths and widths of each pasture are
case 1
x=53.94 ft
y=278.09 ft

case 2
x=208.56 ft
y=71.92 ft