Question

the length of a rectangular sign is 6 inches more than half it’s width. the area of this sign is 432 square inches. write an equation in one variable that could be used to find the number of inches in the dimensions of this sign

Answer 1

Dimensions of Rectangular sign is
`L=18inch,\ W=24inch.`

Explanation:

Given that,

Area of rectangular sign is
`432` square inches.

From the question,

Let the width of rectangular sign is
`x` inch.

So, Length of rectangular sign is
`=(1)/(2)* x +6 =(x)/(2)+6`

Area of rectangle
`= length * width`

Now,
`((x)/(2)+6)* x=432`

⇒
`(x^(2) )/(2) +6x=432`

⇒
`x^(2) +12x=864`

⇒
`x^(2) +12x-864=0`

⇒
`x^(2) +36x-24x-864=0`

⇒
`x(x+36)-24(x+36)=0`

⇒
`x=24,-36`

Neglecting the negative value of
`x` because length can't be negative.

Here, Width of rectangular sign is
`24` inch.

And length of rectangular sign is
`(24)/(2)+6=12+6 =18` inch.

Therefore, Dimensions of Rectangular sign is
`L=18inch,\ W=24inch.`