Question

The length of a rectangle is 3 inches more than the width. The area is 10 square inches. Find the dimensions

Answer 1

Answer:

Width = 2

Length = 5

Step-by-step explanation:

let A be the area of the rectangle

   L be the length of the rectangle

   w be the width of the rectangle

Formula: ‘area of a rectangle’

A = L × w

…………………………………………………

A = L × w

⇔ 10 = (w + 3) × w

⇔ 10 = w² + 3w

⇔ w² + 3w - 10 = 0  

Solving the quadratic equation w² + 3w - 10 =  0 :

Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49

then √Δ = 7

$\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2$

  $or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5$

-5 is not valid ,because w represents the width

which must be a positive number

Then  w = 2

Conclusion:

Width = 2

Length = 2 + 3 = 5