Question

the perimeter of a rectangle is 26 inches. The length of the rectangle is one inch more than twice the width. Find the length and width of a rectangle.

Answer 1

The length is 9, the width is 4.

Explanation:

Assume that the length is
`a`, the width is
`b`.

The perimeter is 26, so
`2(a+b) = 26`.

The length is one inch more than twice the width, so
`a - 2b = 1`.

By solving the system of equations below we get the answer:

`\left \{ {{2(a+b)=26} \atop {a-2b=1}} \right. \\\left \{ {{2a + 2b=26} \atop {a-2b=1}} \right. \\\left \{ {{3a=27} \atop {a-2b=1}} \right. \\\left \{ {{a=9} \atop {9-2b=1}} \right. \\\left \{ {{a=9} \atop {b=4}} \right.`

Answer 2

The width would be 4 and the length would be 9.

I got this answer based off of trial and error.

The question says..

"The length of the rectangle is one inch more than twice the width."

So we will take the width we guess times in by 2 and add one to get the length

ex. W × 2 + 1 = length

ex. 4 × 2 + 1 = length ← What I did

Checking perimeter

4 + 4 + 9 + 9 = 26cm

Formula: W + W + L + L = 26 cm