Question

A rectangle’s length is 2 units more than twice its width. Its area is 40 square units. The equation w(2w + 2) = 40 can be used to find w, the width of the rectangle.

Answer 1

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Answer 2

Answer: Value of w is 4 units and the equation is correct.

Explanation:

Let width of a rectangle be 'w'.

Let length of a rectangle be '2w+2'.

Since we have given that

Area of rectangle = 40 square units.

As we know the formula for "Area = Length × Breadth" :

So, it becomes,

`40=w(2w+2)\\\\40=2w^2+2w\\\\20=w^2+w\\\\w^2+w-20=0\\\\w^2+5w-4w-20=0\\\\w(w+5)-4(w+5)=0\\\\(w+5)(w-4)=0\\\\either\ w=-5\ or\ w=4`

But dimension can't be negative.

So, w must be 4 units.

Hence, Value of w is 4 units and the equation is correct.