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The base of a rectangle is 4 more than the height. The area of the rectangle is 15 square inches. What are the dimensions of the rectangle to the nearest tenth of an inch?

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vicky6089

The dimensions are 6.4 by 2.4. I set up a quadratic equation and solved using the quadratic formula. Take a look at my picture if you want to know how I set the equation up

Height of the rectangle is 2.4 inches and                                                  base of the rectangle is 6.4 inches

What is a rectangle?

Any 2-dimensional figure in which the opposite sides are equal and parallel and each angle is a right angle is called a rectangle.

  • Area of a rectangle = Length x breadth

                              or we can say, base x height

What are the dimensions of the rectangle?

Let the height of the rectangle be H inches.

  • According to the problem,  the base of a rectangle is 4 more than the height .            
  • ∴ Base = ( 4 + H)
  • Area of the rectangle = 15 square inches

∴  H(4+H) =15

⇒H² + 4H - 15 =0

Now, solving the quadratic equation by Shreedhar Acharya formula

H = [tex]\frac{-4+\sqrt{16 + 60} }{2 }[/tex]   or  [tex]\frac{-4-\sqrt{16 + 60} }{2 }[/tex]

⇒ H = 2.35 or -6.35

  • Since length cannot be negative, so H = -6.35 is rejected.

∴ H = 2.4 inches

Base = (4 + 2.4) inches = 6.4 inches

So, height of the rectangle is 2.4 inches and base of the rectangle is 6.4 inches                

You can find more details on:   https://brainly.com/question/2607596  

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