Question

Problem: A carpenter is commissioned to build a chalk board with an area of 50
square feet. The client wants the length to be 5 feet longer than its width. Is it
possible?
xft
(x + 5) ft
Answer the following questions:
1. Write the mathematical sentence that represents the area of the chalk board.
2. Simplify the equation and write it in standard form of quadratic equation.
3. Solve the discriminant of the quadratic equation in #2.
4. is the discriminant a positive or a negative?
5. To answer whether the client's request is possible or not, we need to go back
to the discriminant. If you are to get the square root of the discriminant in
#3, is there a possible value that can represent the width of the board? If
there is, then the client's request is possible. If otherwise, then it is not
possible.​

Answer 1

Given : A carpenter is commissioned to build a chalk board with an area of 50  square feet.  

The client wants the length to be 5 feet longer than its width

To Find :  Is it  possible ?

if possible then find width and length

Solution:

Let say width  of chalkboard = W feet

Length of chalk Board = W + 5 Feet  

Area of Chalk Board = W(W + 5)  sq feet

= W² + 5W

area of chalk board = 50 sq feet

=> W² + 5W  = 50

=> W² + 5W  - 50 = 0

D = 5² - 4(1)(-50)  =  25 + 200  = 225

discriminant   is positive

 W² + 5W  - 50 = 0

=>   W² + 10W - 5W  - 50 = 0

=> W(W + 10) - 5(W + 10) = 0

=> ( W + 10)(W - 5) = 0

=> W = -10 , 5

-ve width not possible hence ignored

So width = 5 feet  

Length = 10  feet

Area = 5 x 10 = 50 sq feet

client's request is possible  

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