The length of a rectangles is 3 inches less than the width. If the perimeter of the rectangle is 14 inches, find the dimensions.

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

8 0

<h3>Answer:</h3>

The answer would be 5 inches for the width and 2 inches for the length of the rectangle.

Step-by-step explanation:

The first step would be to write an equation:

2x+ 2(x-3) = 14 inches

Next do the distributive property:

2x+ 2(x-3) = 14 inches ---> 2x+ 2x-6 = 14 inches

After that, combine like terms:

2x+ 2x-6 = 14 inches ---> 4x-6 = 14 inches

Then, add 6 to both sides:

4x-6 = 14 inches ---> 4x-6+(6) = 14 inches+(6) ---> 4x = 20 inches

Following this, divide both sides by 4:

4x = 20 inches ---> 4x÷(4) = 20 inches÷(4) ---> x = 5 inches

You now have the side length of the rectangle's width.

Lastly, find the length.

5 - 3 = 2 inches

To double-check, check with the equation.

2x+ 2(x-3) = 14 inches ---> 2(5)+ 2(5-3) = 14 inches --->

2(5) +2(2) = 14 inches ---> 10+4 = 14 inches ---> 14=14 inches

The answer is correct.

You might be interested in

the pitch, or frequency, of a vibrating string varies directly with the square root of the tension. if a string vibrates at a fr

Naily [24]

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\begin{array}{llll}
\stackrel{frequency}{f}\textit{ of a vibrating string varies directly}\\
\qquad \qquad \textit{with the square root of the tension }\stackrel{tension}{t}
\end{array}$

$\bf f=k\sqrt{t}\quad \textit{we also know that }
\begin{cases}
f=300\\
t=8
\end{cases}\implies 300=k\sqrt{8}
\\\\\\
\cfrac{300}{\sqrt{8}}=k\implies \cfrac{300}{\sqrt{2^2\cdot 2}}=k\implies \cfrac{300}{2\sqrt{2}}=k\implies \cfrac{150}{\sqrt{2}}=k
\\\\\\
\textit{and we can \underline{rationalize} it to }\cfrac{150\sqrt{2}}{2}\implies 75\sqrt{2}=k$

$\bf thus\qquad f=\stackrel{k}{75\sqrt{2}}\sqrt{t}\implies \boxed{f=75\sqrt{2t}}\\\\
-------------------------------\\\\
\textit{now, when t = 72, what is \underline{f}?}\qquad f=75\sqrt{2(72)}$

5 0

3 years ago

Read 2 more answers

What are the two smallest consecutive odd integers whose sum is greater than 17

Mice21 [21]

Answer:

9 and 11

Step-by-step explanation:

5 0

3 years ago

Indicate whether the measures 3.1, 4.8, and 10.2 can be the side lengths of a triangle. If they can, classify the triangle.

stira [4]