Question

Mr. Johnson currently has a square garden. It is in his garden and into a range of 5 feet shorter than three times shorter than times it width. He decides that the perimeter should be 70 feet. Determine the dimensions, in feet, of his new garden

Answer 1

Answer:

The Dimension of new garden is $25 \ feet\ \times 10\ feet.$

Step-by-step explanation:

Given:

Perimeter of new garden = 70 feet.

Let the length of the new garden be 'l'.

Also Let the width of the new garden be 'w'.

We need to find the dimension of new garden.

Now Given:

Length is 5 feet shorter than three times it width.

framing the equation we get;

$l =3w-5 \ \ \ \ equation\ 1$

Now we know that;

Perimeter of rectangle is equal to twice the sum of length and width.

framing in equation form we get;

$2(l+w)=70$

Now Diving both side by 2 using Division property of equality we get;

$\frac{2(l+w)}2=\frac{70}{2}\\\\l+w =35$

Now Substituting equation 1 in above equation we get;

$3w-5+w=35\\\\4w-5=35$

Adding both side by 5 Using Addition Property of equality we get'

$4w-5+5=35+5\\\\4w=40$

Now Diving both side by 4 using Division property of equality we get;

$\frac{4w}{4}=\frac{40}{4}\\\\w=10\ ft$

Now Substituting the value of 'w' in equation 1 we get;

$l =3w-5\\\\l =3\times10-5\\\\l = 30-5\\\\l= 25\ ft$

Hence The Dimension of new garden is $25 \ feet\ \times 10\ feet.$