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a square has an area of 49 square inches. if the same amount is added to the length and removed from the width, the resulting rectangle has an area of 45 square inches. find the dimensions of the rectangle.

User Ankanna
by
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1 Answer

3 votes

Answer:

length = 9 in

width = 5 in

Explanation:

Algebraic equations and solving:

  • First find the side of square from the given area.
  • Frame the expression for length and width with the help of the side of square.
  • Frame the equation for finding the area of rectangle.
  • Now, by solving the equation, we can find the dimensions of the rectangle.

Area of square =side * side

Side² = 49

Side = √49

= 7 inches

Let the measurement added to the length and removed from the width be 'x'.

length = (7 + x) in

width = (7 -x )in

Area of rectangle = length *width

length * width = 45 square inches

(7 + x)(7-x) = 45

{Identity: (a + b)(a -b) = a² - b² where a = 7 & b = x}

7² - x² = 45

49 - x² = 45

-x² = 45 - 49

-x² = - 4

x² = -4 ÷ (-1)

x² = 4

x = √4

x = 2

Dimension of the rectangle:

length =7 + 2 = 9 in

width = 7 - 2 = 5 in

User Ankesh Anand
by
8.2k points

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