Answer:
[tex]\sf Perimeter =64.75 \textsf{ ft } [/tex]
[tex]\sf Area =213.90625 \textsf{ ft }^2 [/tex]
Step-by-step explanation:
Let's denote the width of the rectangle as [tex]\sf w [/tex] and the length as [tex]\sf l [/tex]. According to the given information:
The ratio of the length to the width is [tex]\sf 5:2 [/tex], which can be expressed as [tex]\sf \dfrac{l}{w} = \dfrac{5}{2} [/tex].
2. The length is 13.875 feet greater than the width, so:
[tex]\sf l = w + 13.875 [/tex].
Now, let's use this information to find the values of [tex]\sf l [/tex] and [tex]\sf w [/tex]. We can set up and solve the system of equations:
[tex]\sf \dfrac{l}{w} = \dfrac{5}{2} [/tex]
[tex]\sf l = w + 13.875 [/tex]
Substitute [tex]\sf l = w + 13.875 [/tex] into the first equation:
[tex]\sf \dfrac{w + 13.875}{w} = \dfrac{5}{2} [/tex]
Cross-multiply:
[tex]\sf 2(w + 13.875) = 5w [/tex]
Simplify:
[tex]\sf 2w + 27.75 = 5w [/tex]
Subtract [tex]\sf 2w [/tex] from both sides:
[tex]\sf 2w + 27.75 -2w = 5w-2w [/tex]
[tex]\sf 27.75 = 3w [/tex]
Divide by 3:
[tex]\sf \dfrac{ 27.75 }{3}=\dfrac{ 3w}{3} [/tex]
[tex]\sf w = 9.25 \textsf{ ft } [/tex]
Now that we have the width [tex]\bold{\sf w }[/tex], we can find the length [tex]\bold{\sf l }[/tex] using [tex]\sf l = w + 13.875 [/tex]:
[tex]\sf l = 9.25 + 13.875 = 23.125 \textsf{ ft} [/tex]
Now, we can calculate the perimeter [tex]\bold{\sf P }[/tex] and the area [tex]\bold{\sf A }[/tex] of the rectangle:
We know that: the formula to calculate the perimeter of a rectangle is:
[tex]\sf P = 2l + 2w [/tex]
where
Now, substitute the value and simplify:
[tex]\sf P = 2(23.125) + 2(9.25) [/tex]
[tex]\sf P =64.75 \textsf{ ft } [/tex]
Therefore, the perimeter of the rectangle is 64.75 ft.
Now,
The formula to calculate the area of the rectangle is:
[tex]\sf A = lw [/tex]
where
Now, substitute the value and simplify:
[tex]\sf A = (23.125)(9.25) [/tex]
[tex]\sf A =213.90625 \textsf{ ft }^2 [/tex]
Therefore, the area of the rectangle is 213.90625 ft².
