Question

(t point) A rectangular garden is 20 ft longer than it is wide. Its area is 7125 . What are its dimensions?

is with equals
and its length equals

Answer 1

`Length =95` feet

`width =75` feet

Explanation:

Let x be the width of a rectangle

Let l be the length of a rectangle

Let A be the area of rectangle

Given.

The garden is 20 feet longer than wide

therefore
`l=20+w=20+x`

Area of rectangle is
`7125`

We know that area of rectangle is

`A = l* w`---------------------(1)

put all known values in equation 1

`7125 = (20+x)* x`

`x^(2) +20x-7125=0`

Find roots of equation by this formula

where
`a=1, b=20, c=-7125`

`x=\frac{-b\pm\sqrt{b^(2)-4ac } }{2a}`

`x=\frac{-20\pm\sqrt{20^(2)-4(1)(-7125) } }{2(1)}`

`x=(-20\pm√(28900 ) )/(2)`

`x=75` or
`x=-95`

check both value in equation 1

`A=(20+75)* 75\\A=7125`

So, the
`x=75` is satisfy the equation 1.

So The length of rectangle =
`20+x` =
`20+75` =
`95` feet

And width is 75 feet