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