Question

A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice the width. What is the length of the plywood’s diagonal? Round your answer to the nearest tenth.

Answer 1

Answer:

The length of the diagonal = 3.6 feet

Step-by-step explanation:

* Lets change the story problem to equation to solve it

- Diagonal in a rectangle is the line which joining two

 opposite vertices in it

- The diagonal , the length and the width formed together right

  angle triangle where the diagonal is the hypotenuse of the

  triangle and the length, the width are the two legs of the

  right angle

- The length of the diagonal d is √(l² + w²) ⇒ Pythagoras theorem

∴ d² = l² + w²

- The diagonal is 2 feet more than the width

∴ d = w + 2

- The length is twice the width

∴ l = w

* Lets substitute the value of d and l in the equation of Pythagoras

∴ (w + 2)² = (2w)² + w² ⇒ solve the bracket

∴ w² + 4w + 4 = 4w² + w² ⇒ collect them in one side and add like term

∴ 4w² + w² - w² - 4w - 4 = 0 ⇒ add the like term

∴ 4w² - 4w - 4 = 0 ⇒ divide all term by 4

∴ w² - w - 1 = 0 ⇒ solve the quadratic using the formula

- In ax² + bx + c = 0

 $x=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}$

∵ a = 1 , b = -1 , c = -1

∴ $x=\frac{-(-1)+\sqrt{(-1)^{2}-4(1)(-1)}}{2(1)}=\frac{1+\sqrt{5}}{2}=1.6feet$

-The value of the width is 1.6 feet

∴ The length = 1.6 × 2 = 3.2 feet

∴ The length of the diagonal = 2 + 1.6 = 3.6 feet