Completing The Square

Question

A sandbox has an area of 45ft^2. The length is 4 feet longer than the width. Find the dimensions of the sandbox. Solve by completing the square

 

Write an equation for the total area

 

Find the dimensions

Answer 1

Hi Justin;

 

L = w+4

Lw = 45

 

w(w+4) = 45

w² + 4w = 45

w² + 4w + 4 = 45-4

(w+2)² = 41

w+2 = ±√41

We can disregard the negative root since

width will be positive.

w = √41 - 2

 

L = w+4 = √41 + 2

 

Dimensions:  √41 + 2 feet by  √41 - 2 feet

 

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