Question

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

Answer 1

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: $d=3w$

Also given is the length of the plywood is three feet more than the width. This is : $l=x+3$

Now, in terms of x we get:

Width = x

Length = (x+3)

Length of Diagonal = 3x

Now applying Pythagorean Theorem

$a^{2}+b^{2}=c^{2}$

$x^{2}+(x+3)^{2}=(3x)^{2}$

$x^{2}+x^{2}+6x+9=9x^{2}$

Solving this we get,

$-7x^{2}+6x+9=0$

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.