Question

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.

Answer 1

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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Answer 2

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

$32\ sections$