Question

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The length of a rectangle is twice its width. Given the length of the diagonal is $5\sqrt{5}$, find the area of the rectangle.

Answer 1

Answer:

Step-by-step explanation:

Width =x

Length = 2*x = 2x

Diagonal = 5√5

Use Pythagorean theorem

Length² + Width² = diagonal²

  (2x)²    + x²        = (5√5)²      

{$(5\sqrt{5})^{2}=5\sqrt{5} *5\sqrt{5}=5*5*\sqrt{5*5}=25*5=75$}

     4x²   + x²        = 75

                      5x² = 75

                        x²  = 75/5

                       x²   = 15

                        x = √15

Width = √15

Length = 2√15

Area of rectangle = length *width

                             = √15 *2√15

                             $= 2* \sqrt{15*15}\\\\= 2*15\\= 30$

                             = 30 square units