Answer:
Area of rectangle = 128 square feet
Step-by-step explanation:
Given:- A rectangle with side(a)=16 feet, side (b) = [tex]\frac{1}{2}[/tex] that links to a square.
perimeter (p) = 48 feet.
To find:- area of the square of the rectangle=?
Now,
[tex]Perimeter\ of\ square\ (p) = (2\times a)+(2\times b)[/tex]
[tex]48=(2\times 16)+(2\times b)[/tex]
[tex]48=32+2b[/tex]
[tex]2b=48-32[/tex]
[tex]2b=16[/tex]
[tex]b=\frac{16}{2}[/tex]
[tex]b=8 feet[/tex] -------(equation 1)
(8 is half of square of 4=16, [tex]4^{2}=16,\ \frac{16}{2} = 8[/tex])
Now, to find the area of square:-
Area of square (A) = Length [tex]\times[/tex] breadth
Area of square (A)= side a [tex]\times[/tex] side b
A= 16 [tex]\times[/tex] 8
[tex]\therefore[/tex]A = 128 square feet
Therefore Area of rectangle = 128 square feet
