Question

The perimeter of a rectangular wooden deck is 90 feet. The deck's length, l, is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck?

Answer 1

Answer:

The system of equation used to find the dimension of the wooden deck in feet are $\left \{ {{l=4w-5} \atop {90=2(l+w)}} \right.$.

Step-by-step explanation:

Given:

Perimeter of deck = 90 feet.

We need to find the system of equation used to determine the dimension in feet of the wooden deck.

Solution:

Let the length of the deck be 'l'.

Let the width of the deck be 'w'.

Now Given:

The deck's length, l, is 5 feet less than 4 times its width, w.

So we can say that;

Length of the deck is equal to 4 times width minus 5.

framing in equation form we get;

$l=4w-5$  ⇒ Equation 1

Now we know that;

Perimeter of the rectangle is given by 2 times Length times width of the rectangular deck.

framing in equation form we get;

$90=2(l+w)$ ⇒ Equation 2

Hence The system of equation used to find the dimension of the wooden deck in feet are $\left \{ {{l=4w-5} \atop {90=2(l+w)}} \right.$.