Question

For a rectangle with a perimeter of 20 cm, the width of the rectangle is one-third its length. Use an equation to find the length and width of the rectangle.

Answer 1

Answer:

Step 1. The perimeter P means adding up all four sides of a rectangle.

Step 2. Let w be the width

Step 3. Let 3w be the length since the width is one-third the length

Step 4. Then P=w+w+3w+3w=8w=20 since the perimeter P is 20 cm.

Step 5. Solving the equation in Step 4 leads to the following steps

Divide by 8 to both sides of the equation

8w%2F8=20%2F8

w=5%2F2 and 3w=15/2 and P=2(5/2+15/2)=20 which is a true statement.

Step 6. ANSWER: The width is 5/2 cm.

I hope the above steps and explanation were helpful.

Answer 2

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{ANSWER}}\mid}}}}$

Given :

>Perimeter of the rectangle = 20cm

>The Width is one third of the length

So,

Let the length be = $\bold{ x }$

then, the breadth will be = $\frac{1}{3} \times x = \bold{\frac{x}{3}}$

To find : The dimensions of the rectangle.

Formula for perimeter of rectangle = $\bold {2 (L + B)}$

So, According to the question, the equation will be :

$\bold{20 = 2 (x + \frac{x}{3})}$

Now, Let's find the value of $x$

$20 = 2(x + \frac{x}{3} ) \\ = > 20 = 2( \frac{ x }{1} + \frac{x}{3} ) \\ = > 20 = 2( \frac{3x + x}{3} ) \\ = > 20 = 2 \times \frac{4x}{3} \\ = > 20 = \frac{8x}{3}$

By Cross Multiplication,

$= > 8x = 20 \times 3 \\ = > x = \frac{20 \times 3}{8} \\ = > x = \frac{60}{8} \\ = > 7.5$

Therefore, Value of $\bold{x = 7.5}$

Hence,

Length = $x$ = 7.5 cm

Breadth = $\frac{x}{3}$ = 2.5 cm