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Arturiano [62]
3 years ago
15

A rectangle patio is surrounded on three sides by a fence. If the areas of the patio is 45 m sq and the total of fence is 19m wh

at is the length and width of the patio?
Mathematics
1 answer:
Eddi Din [679]3 years ago
3 0
LW = 45
L + 2W = 19
L = 19-2W

substituting for L :-
W(19-2W) = 45

-2W^2 + 19W = 45

2W^2 - 19W + 45 = 0 
W = 5 or 4.5

If W = 5, L = 9
If W = 4.5, L = 10

So there are 2 possible answers.


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Since, PS and QR are parallel, we know that <QRP is equal to <RPS.  Therefore, we can solve for y by setting the two equations equal to each other.

5y+14=8y-13

<em>*Subtract 5y from both sides to isolate the variable*</em>

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<em>*Add 13 to both sides*</em>

27=3y

<em>*Divide both sides by 3*</em>

9=y


Now, plug in 9 for y in the equation 8y-13 to find the measure of that angle.

8(9)-13

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Now, the sum of the angles in any triangle is equal to 180 degrees.  We can use this knowledge to set up an equation to solve for x.

3x+2x+1+59=180

<em>*Combine like terms*</em>

5x+60=180

<em>*Subtract 60 from both sides*</em>

5x=120

<em>*Divide both sides by 5*</em>

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Now, we can find <RSP by pluggin 24 in for x.

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<RSP=49 degrees


Hope this helps!!

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