Question

The length of a rectangle is 2 cm more than

3 times its width. Its area is 85 cm?. Find the
dimensions of the rectangle.

Answer 1

Width of rectangle = 5 cm

Length of rectangle = 17 cm

Explanation:

Let the dimensions of rectangle:

Width of rectangle = x

Length of rectangle = 3x+2

Area of rectangle = 85 cm

We need to find dimensions of rectangle i.e length and width.

The formula used is:
`Area\:of\:rectangle=Length* Width`

Putting values and finding dimensions

`Area\:of\:rectangle=Length* Width\\85=3x+2 * x\\85=3x^2+2x\\The\;equation\:will\:be:\\3x^2+2x-85=0`

Now, finding value of x using quadratic formula:

`x=(-b\pm √(b^2-4ac))/(2a)`

We have, a =3, b =2 and c=-85

`x=(-2\pm √((2)^2-4(3)(-85)))/(2(3))\\x=(-2\pm √(4+1020))/(6)\\x=(-2\pm √(1024))/(6)\\x=(-2\pm 32)/(6)\\x=(-2+ 32)/(6)\:or\:x=(-2- 32)/(6)\\x=5\:or\:x=-5.6`

So, we get x = 5 and x = -5.6

But since the width of rectangle cannot be negative so, we would consider x = 5

Now, the dimensions of rectangle will be:

Width of rectangle = x = 5 cm

Length of rectangle = 3x+2 = 3(5) + 2 = 15+2 = 17 cm