Question

The length of a rectangle is 5 centimeters less than twice its width. The perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle?


A. length = 7 cm; width = 6 cm


B. length = 4 cm; width = 9 cm


C. length = 6 cm; width = 7 cm


D. length = 5 cm; width = 5 cm

Answer 1

A. length = 7 cm; width = 6 cm

Use w to represent width, p as perimeter, and l for length.

l = 2w - 5

2l + 2w = p
2(2w - 5) + 2w = 26
4w - 10 + 2w = 26
6w - 10 = 26
6w = 36
w = 6

The only option with a width of 6 is A.
To check your answer, you can plug it in.
2(6) - 5 = 12 - 5 = 7

Hope this helps.

Answer 2

The correct option is $\boxed{\text{\bf option C}}$ i.e., the length is $6\text{ cm}$ and breadth is $7\text{ cm}$.

Further explanation:

The perimeter of arectangle is calculated as follows:

$\boxed{\text{Perimeter}=2\cdot (l+b)}$

Here, $l$ is the length and $b$ is the breadth of the rectangle.

Given:

The length of the rectangle is $5\text{ cm}$ less than twice its breadth and the perimeter of the rectangle is $26\text{ cm}$.

Calculation:

Step 1:

First we write the dimensions in the form of variable $x$.

Consider $x$ as the breadth of the rectangle and $y$ as the length of the rectangle.

As per the question the length is $5\text{ cm}$ less than twice its breadth.

Therefore, the length can be expressed in the form of the equation as follows:

$\boxed{y=2x-5}$  …… (1)

Step 2:

Now, we have to calculate the dimensions of the rectangle.

So, substitute $l=2x-5$ and $b=x$ in the formula of the perimeter of the rectangle to obtain the value of $x$.

$\begin{aligned}\text{Perimeter}&=2\cdot (l+b)\\26&=2\cdot (2x-5+x)\\26&=2\cdot (3x-5)\\26&=6x-10\\6x&=26+10\\6x&=36\\x&=6\end{aligned}$  

Therefore, the breadth of the rectangle is $6\text{ cm}$.

Now, substitute $x=5$ in the equation (1) to obtain the value of the length.

$\begin{aligned}l&=2x-5\\&=(2\cdot 6)-5\\&=12-5\\&=7\end{aligned}$

Therefore, the length of the rectangle is $7\text{ cm}$.

Thus, the correct option is $\boxed{\text{\bf option C}}$ i.e., the length is $6\text{ cm}$ and breadth is $7\text{ cm}$.

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Answer details:

Grade: Junior school

Subject: Mathematics

Topic: Area and Perimeter  

Keywords: Length, breadth, perimeter, area, side, dimensions, rectangle, shapes, figure, triangle, square, equation, variable, constant, twice, area, mensuration.