Question

In a rectangle, the ratio of the length to the width is 5: 2. The length of the
rectangle is 13.875 feet greater than the width. What are the perimeter and the area of the rectangle?

Answer 1

Answer:

$\sf Perimeter =64.75 \textsf{ ft }$

$\sf Area =213.90625 \textsf{ ft }^2$

Step-by-step explanation:

Let's denote the width of the rectangle as $\sf w$ and the length as $\sf l$. According to the given information:

The ratio of the length to the width is $\sf 5:2$, which can be expressed as $\sf \dfrac{l}{w} = \dfrac{5}{2}$.

2. The length is 13.875 feet greater than the width, so:

$\sf l = w + 13.875$.

Now, let's use this information to find the values of $\sf l$ and $\sf w$. We can set up and solve the system of equations:

$\sf \dfrac{l}{w} = \dfrac{5}{2}$

$\sf l = w + 13.875$

Substitute $\sf l = w + 13.875$ into the first equation:

$\sf \dfrac{w + 13.875}{w} = \dfrac{5}{2}$

Cross-multiply:

$\sf 2(w + 13.875) = 5w$

Simplify:

$\sf 2w + 27.75 = 5w$

Subtract $\sf 2w$ from both sides:

$\sf 2w + 27.75 -2w = 5w-2w$

$\sf 27.75 = 3w$

Divide by 3:

$\sf \dfrac{ 27.75 }{3}=\dfrac{ 3w}{3}$

$\sf w = 9.25 \textsf{ ft }$

Now that we have the width $\bold{\sf w }$, we can find the length $\bold{\sf l }$ using $\sf l = w + 13.875$:

$\sf l = 9.25 + 13.875 = 23.125 \textsf{ ft}$

Now, we can calculate the perimeter $\bold{\sf P }$ and the area $\bold{\sf A }$ of the rectangle:

We know that: the formula to calculate the perimeter of a rectangle is:

$\sf P = 2l + 2w$

where

• P = perimeter,
• l = length and
• w = width

Now, substitute the value and simplify:

$\sf P = 2(23.125) + 2(9.25)$

$\sf P =64.75 \textsf{ ft }$

Therefore, the perimeter of the rectangle is 64.75 ft.

Now,

The formula to calculate the area of the rectangle is:

$\sf A = lw$

where

• A = Area,
• l = length and
• w = width

Now, substitute the value and simplify:

$\sf A = (23.125)(9.25)$

$\sf A =213.90625 \textsf{ ft }^2$

Therefore, the area of the rectangle is 213.90625 ft².