Question

Sally is having a problem with her puppy leaving the yard so she decides to build a new fence. the length of the yard is 10 feet more than 2 times the width. she needs 56 feet of fencing to do the job. find the length of the yard.

Answer 1

The length of the yard is $\boxed{22\text{ feet}}$.

Further explanation:

It is given that Sally is having a problem with her puppy leaving the yard so she decides to build a new fence.

The length of the yard is $10$ feet more than $2$ times the width.

She needs $56$ feet of fencing to do the job.

Consider the length and width of the yard as $x$ feet and $y$ feet respectively.

And it is given that the length of yard is $10$ feet more than $2$ times the width.

So, the equation for length is as follows:

$\boxed{x=2y+10}$         ....(1)

Therefore, the perimeter is calculated as follows:

$\begin{aligned}P&=(2\times \text{length})+(2\times \text{breadth})\\&=2x+2y\\&=2(2y+10)+2y\end{aligned}$  ...(2)

Also given that she needs $56$ feet of fencing to do the job.

Thus, the perimeter of the yard is $56$ feet.

Substitute the value of perimeter in equation (2) to obtain the value of $y$ as  follows:

$\begin{aligned}2(2y+10)+2y&=56\\4y+20+2y&=56\\6y&=56-20\\6y&=36\\y&=6\end{aligned}$

The value of $y$ is $6$ feet.

Therefore, the width of the fence is $6$ feet.

Now, substitute the value of $y$ in equation (1) to find the value of $x$ as,

$\begin{aligned}x&=(2\times 6)+10\\&=12+10\\&=22\end{aligned}$

Therefore, the length of the yard is $\boxed{22\text{ feet}}$.

Learn more

1. Problem on the whole numbers are positive integers brainly.com/question/1852063.

2. Problem on the adding and simplifying the numbers brainly.com/question/894273

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Mensuration

Keywords: Perimeter, area, rectangle, square, triangle, cube, cuboid, rational numbers, irrational numbers, real numbers, whole numbers, natural numbers, fraction, integers.

Answer 2

Let x be the yard length, then if the length of the yard is 10 feet more than 2 times the width, the length of the yard is 2x+10. The perimeter is 2 lengths + 2 widths, so P=2x+2(2x+10) .

Since Sally needs 56 feet of fencing to do the job, P=56 ft. and

2x+2(2x+10)=56,

2x+4x+20=56,

6x=56-20,

6x=36,

x=6 ft. and 2x+10=12+10=22 ft.

Answer: The length of the yard is 22 feet