Question

the perimeter of a rectangle is 50 inches the length l is twice the width w. what is the area of the rectangle?? ❗️show work❗️

Answer 1

Hey. Let me help you on this one.

In order for us to solve this problem, we will need to set up an equation which we can solve later. I will also be attaching an image with the work shown in case you don't understand my explanation. Make sure to read over it since it will help you with your studies.

We know that the length is twice the width, meaning that $a=2b$, with "a" standing for length, and "b" standing for width. Now that we have formed an equation for length, we can actually form an equation for perimeter.

$P=2(2b)+2b$

Let's simplify the equation so it's easier and less confusing for us to solve it.

$50=6b$

Let's divide 6 from both sides, thus eliminating all variables except for b on the right side.

$8.3=b$

"3" in 8.3 is repeating. This is very important to remember. Now, we know the width of the triangle. Let's find the length of the triangle so we can then multiply both numbers together and find the area.

$a=8.3*2$
$a=16.6$

"6" in 16.6 is repeating as well. It's crucial to remember as well. We know the values now, meaning that we can find the area of the rectangle.

$S=16.6*8.3$
$S=138.8$

Answer: Area of the rectangle is 138.8 (with 8 repeating).