Answer:
The area of the table is [tex]1,008\ in^{2}[/tex]
Step-by-step explanation:
Let
x----> the length of the rectangular table
y---> the width of the rectangular table
we know that
The perimeter is equal to
[tex]P=2(x+y)[/tex]
[tex]P=132\ in[/tex]
so
[tex]132=2(x+y)[/tex]
[tex]66=x+y[/tex] ------> equation A
[tex]x=1\frac{3}{4}y[/tex]
[tex]x=\frac{1*4+3}{4}y[/tex]
[tex]x=\frac{7}{4}y[/tex] ---> equation B
substitute equation B in equation A and solve for y
[tex]66=\frac{7}{4}y+y[/tex]
[tex]66=\frac{11}{4}y[/tex]
[tex]y=66*4/11=24\ in[/tex]
Find the value of x
[tex]x=\frac{7}{4}(24)=42\ in[/tex]
Find the area of the table
The area is equal to
[tex]A=xy=(42)(24)=1,008\ in^{2}[/tex]
