Answer:
(a) [tex]Perimeter = 32.2\ cm[/tex]
(b) 100
Step-by-step explanation:
Solving (a):
Given
Shape: Rectangle
[tex]Area = 64.8[/tex]
Required
Calculate the perimeter.
Area is calculated as:
[tex]Area = L * W[/tex]
Where
[tex]L = Length[/tex] and [tex]W = Width[/tex]
Substitute 64.8 for Area
[tex]64.8 = L * W[/tex]
Make L the subject:
[tex]L = \frac{64.8}{W}[/tex]
Perimeter is calculated as:
[tex]P = 2 * (L + W)[/tex]
Substitute 64.8/W for L
[tex]P = 2 * (\frac{64.8}{W} + W)[/tex]
[tex]P = \frac{129.6}{W} + 2W[/tex]
To solve further, we take the derivative of P and set it to 0, afterwards.
[tex]dP = -\frac{129.6}{W^2} + 2[/tex]
Set to 0
[tex]0 = -\frac{129.6}{W^2} + 2[/tex]
Collect Like Terms
[tex]\frac{129.6}{W^2} = 2[/tex]
Cross Multiply:
[tex]2W^2= 129.6[/tex]
Divide through by 2
[tex]W^2 = 64.8[/tex]
Take square roots
[tex]W = \sqrt{64.8[/tex]
[tex]W = 8.05[/tex]
Recall that:
[tex]L = \frac{64.8}{W}[/tex]
So:
[tex]L= \frac{64.8}{8.05}\\[/tex]
[tex]L= 8.05[/tex]
The perimeter is:
[tex]Perimeter = 2 * (8.05 + 8.05)[/tex]
[tex]Perimeter = 2 * (16.10)[/tex]
[tex]Perimeter = 32.2\ cm[/tex]
Solving (b):
Given
((1 Group of 10 tenths) and (1 group of 8 tenths))/(6 groups of 3 tenths)
Required
Solve
[tex]Tenths = \frac{1}{10}[/tex]
So, the expression becomes:
((1 Group of [tex]10 * \frac{1}{10}[/tex]) and (1 group of [tex]8 * \frac{1}{10}[/tex]))/(6 groups of [tex]3 * \frac{1}{10}[/tex])
This gives:
((1 Group of [tex]\frac{10}{10}[/tex]) and (1 group of [tex]\frac{8}{10}[/tex]))/(6 groups of [tex]\frac{3}{10}[/tex])
Group means product, so the expression becomes:
[tex]\frac{(1 * \frac{10}{10} \ and\ 1 * \frac{8}{10})}{6 * \frac{3}{10}}[/tex]
And, as used here means addition
[tex]\frac{(1 * \frac{10}{10} + 1 * \frac{8}{10})}{6 * \frac{3}{10}}[/tex]
Simplify:
[tex]\frac{(1 * 1 + 1 * 0.80)}{6 *0.30}[/tex]
[tex]\frac{(1 + 0.80)}{1.80}[/tex]
[tex]\frac{1.80}{1.80}[/tex]
[tex]= 1.00[/tex]
