Question

A rectangular piece of plywood has a diagonal that measures three feet more than the width. The length of the plywood is three times the width. What is the length of the plywood diagonal?

Answer 1

Answer:

The length of the plywood diagonal is $4.387\ units$

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

$d=\sqrt{x^{2}+y^{2} }$ -----> equation A

$d=y+3$ ----> equation B

$x=3y$ -----> equation C

substitute equation C and equation B in equation A and solve for y

$(y+3)=\sqrt{(3y)^{2}+y^{2}}$

squared both sides

$(y+3)^{2}=10y^{2}\\ \\y^{2}+6y+9=10y^{2}\\ \\9y^{2}-6y-9=0$

Solve the quadratic equation by graphing

The solution is $y=1.387\ units$

see the attached figure

Find the value of d

$d=y+3$----- > $d=1.387+3=4.387\ units$