Answer:
The length of diagonal is 4.922 feet.
Step-by-step explanation:
Let the width be = w
Let the diagonal be = d
Let the length be = l
Given is that the diagonal measures three times the width, this gives: [tex]d=3w[/tex]
Also given is the length of the plywood is three feet more than the width. This is : [tex]l=x+3[/tex]
Now, in terms of x we get:
Width = x
Length = (x+3)
Length of Diagonal = 3x
Now applying Pythagorean Theorem
[tex]a^{2}+b^{2}=c^{2}[/tex]
[tex]x^{2}+(x+3)^{2}=(3x)^{2}[/tex]
[tex]x^{2}+x^{2}+6x+9=9x^{2}[/tex]
Solving this we get,
[tex]-7x^{2}+6x+9=0[/tex]
We will use quadratic formula to solve this and get the answer,
x = 3/7 +/- (12√2) / -14
x = 1.64075 or x = -0.783612(neglect this negative value)
So, x = 1.64075 feet
Now length of diagonal is 3x = 3*1.64075 = 4.922 feet
So, length of diagonal is 4.922 feet.
