11 June, 09:58

# The length of a rectangle is 2 units more than the width. The area of the rectangle is 63 units. What is the length, in units, of the rectangle?

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1. 11 June, 11:21
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Length = 9units

Width = 7units

Step-by-step explanation:

It is said that the length is 2units more than the width

Assume that the width is x, then the length will be 2 + x

ie

Width = x

Length = 2 + x

Area of the rectangle = 63units

Area of rectangle = l * b

l - length of the rectangle

b - width of the rectangle

A = l * b

63 = (2 + x) * x

63 = (2 + x) x

63 = 2x + x^2

Let's rearrange it

x^2 + 2x - 63 = 0

Let's find the factor of 63

A factor that can be multiplied to give - 63 and that can be added to give + 2

Let's use - 7 and + 9

x^2 - 7x + 9x - 63 = 0

Separate with brackets

(x^2 - 7x) + (9x - 63) = 0

x (x - 7) + 9 (x - 7) = 0

(x + 9) (x - 7) = 0

(x + 9) = 0

(x - 7) = 0

x + 9 = 0

x = - 9

x - 7 = 0

x = 7

Note: the length of a rectangle can not be negative

So therefore,

x = 7

Length = 2 + x

= 2 + 7

= 9units

Width = x

= 7units