The length of a rectangle is 6 in. more than its width. Its area is 40 sq. in. How do you find the width of the rectangle?

1 Answer
Suren Abreu
Dec 9, 2016

The width of the rectangle is #4# inches.

Explanation:

We consider the width of the rectangle as #x# which will make the length #(x+6)#. Since we know the area, and the formula of a rectangle's area to be length #xx# breadth, we can write:

#x xx (x+6)=40#

Open the brackets and simplify.

#x^2+6x=40#

Subtract #40# from both sides.

#x^2+6x-40=0#

Factorise.

#x^2+10x-4x-40=0#

#x(x+10)-4(x+10)=0#

#(x-4)(x+10)=0#

#x-4=0# and #x+10=0#

#x=4# and #x=-10#

The only possibility in the above problem is that #x=4#.

That will make the width #4# and the length #(x+6)# which is #10#, and the area #(4xx10)# which is #40#.

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