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

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

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`