Answer:
D
Step-by-step explanation:
The perimeter of a rectangle is given by the formula:
[tex]P=2(l+w)[/tex]
From our figure, our length is (2s-5) and our width is (4s-13). So, let's substitute (2s-5) for l and (4s-13) for w. This yields:
[tex]P=2((2s-5)+(4s-13))[/tex]
We also know that the perimeter is 108. So, substitute that for P:
[tex]108=2(2s-5+4s-13)[/tex]
Solve for s. We can first divide everything by 2:
[tex]54=2s-5+4s-13[/tex]
Combine like terms:
[tex]54=(2s+4s)+(-5-13)[/tex]
Add or subtract:
[tex]54=6s-18[/tex]
Add 18 to both sides:
[tex]72=6s[/tex]
Divide both sides by 6:
[tex]s=12[/tex]
So, the value of s is 12.
Now, substitute this back in to find our length and width:
[tex]l=2s-5[/tex]
Substitute 12 for s:
[tex]l=12(2)-5[/tex]
Multiply and subtract:
[tex]l=24-5=19[/tex]
Now, let's find the width:
[tex]w=4s-13[/tex]
Substitute 12 for s:
[tex]w=4(12)-13[/tex]
Multiply and subtract:
[tex]w=48-13=35[/tex]
So, our length is 19 and our width is 35.
The choice that reflects this is D.
And we're done!
