Answer to Question #142673 in Algebra for aparna

Question

The large square consists of four identical rectangles and one square. The area of the small square is half the area of one rectangle. Write and solve the equation to find the area of one rectangle , and then find the dimensions of the rectangle if the total area of a large square is 81ft^2.

Answer 1

Solution.

$S(large square)=81 (ft^2).$

Let the area of small square is $x ft^2.$ Then, the area of one rectangle is $2*x ft^2.$

The equation of total area is:

$x+2*x+2*x+2*x+2*x=81; \newline 9*x=81;\newline x=9.$

The area of one rectangle is:

$S(one rectangle)=2*x=2*9=18 (ft^2).$

Let the side of the square is $a.$ The area of the square is:

$S(square)=a^2; \newline a^2=9; \newline a=3 (ft).$

Area of the rectangle is 2-dimensional: it has a length and a width.

The length $l$ and width $w$ of one rectangle are:

$l=2*a=2*3=6 (ft); \newline w=a=3 (ft).$

Answer: $S (one rectangle)=18 (ft^2), l=6 (ft), w=3 (ft).$