Fill in the blanks:

Mark’s garden is a rectangle that is 4a^2 + 96a + 15 meters long and 4a^2 + 24a + 15 meters wide. If Mark decides to fence his garden, the total length of fencing material required would be meters. If he uses prebuilt fence sections that are 50 centimeters wide, he will need sections.

So for a rectangle, perimeter = 2L + 2W.

Plugging in, we get

P = 2 [ (4a + 96) / (a + 15) ] + 2 [ (4a + 24) / (a + 15) ]

= (8a + 192 + 8a + 48) / (a + 15)

= (16a + 240) / (a + 15)

= 16(a + 15) / (a + 15)

= 16 meters.

So if Mark buys the sections,

50 cm = 0.5 meter, so he will need 32 sections.

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calculista calculista · Answer 2 · 2018-09-04T13:26:11-04:00

Let

x--------> the length side of the rectangle

y--------> the width side of the rectangle

we know that

The perimeter of a rectangle is equal to

\(P=2x+2y\)

\(x=(4a + 96)/(a + 15)\)

\(y=(4a + 24)/(a + 15)\)

Substitute the values of x and y in the formula of perimeter

\(P=2*[(4a + 96)/(a + 15)]+2*[(4a + 24)/(a + 15)]\)

\(P=[(8a + 192)/(a + 15)]+[(8a + 48)/(a + 15)]\)

\(P=[(16a + 240)/(a + 15)]\)

\(P=16*[(a + 15)/(a + 15)]\)

\(P=16\ m\)

therefore

the answer part a) is

the total length of fencing material required would be \(16\ m\)

Part b) Divide the perimeter by the width of the prebuilt fence sections

so

\(\frac{16}{0.50} = 32\ sections\)

therefore

the answer Part b) is

\(32\ sections\)