Question

The length of the rectangle is 8 cm greater than its width find the dimensions of the rectangle if it's area is 105cm^2

Answer 1

Greetings!

Answer:

Width = 7

Length = 15

Step-by-step explanation:

Let x be the width value:

Because the length is 8cm bigger than the width(x), this can be shown by:

Length = x + 8

If you recall the equation for the area of a rectangle:

Area = length x width

Simply plug the known values in:

105 = (x + 8) * x

(x * x) + (8 * x) = 105

x² + 8x = 105

Move the +105 to the other side making it a -105, meaning that this is now a quadratic:

x² + 8x - 105 = 0

Factorise this:

(x + 15) ( x - 7)

So x = -15 or x = 7

X has to be 7 because you cannot have a negative measurement.

This means that:

The width = 7

And the length = 7 + 8 = 15

Hope this helps!