Answer:
The length of the plywood diagonal is [tex]4.387\ units[/tex]
Step-by-step explanation:
Let
x-----> the length of the rectangle
y----> the width of the rectangle
we know that
The diagonal of rectangle is equal to
[tex]d=\sqrt{x^{2}+y^{2} }[/tex] -----> equation A
[tex]d=y+3[/tex] ----> equation B
[tex]x=3y[/tex] -----> equation C
substitute equation C and equation B in equation A and solve for y
[tex](y+3)=\sqrt{(3y)^{2}+y^{2}}[/tex]
squared both sides
[tex](y+3)^{2}=10y^{2}\\ \\y^{2}+6y+9=10y^{2}\\ \\9y^{2}-6y-9=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]y=1.387\ units[/tex]
see the attached figure
Find the value of d
[tex]d=y+3[/tex]----- > [tex]d=1.387+3=4.387\ units[/tex]
