An amusement park owner wants to place a new rectangular billboard to
inform visitors of their new attractions. Suppose the length of the
billboard to be placed is 4 m longer than its width and the area is 96 m2
.
What will be the length and the width of the billboard?
Answers
Answer:
Length = x + 4
Width = x
Area = 96 m²
Area = Length(Width)
96 = (x+4)(x)
x² + 4x - 96 = 0
Finding Roots:
Factors of 96 : 1:96, 2:48, 3:32, 4:24, 6:16, 8:12
Find any pair of factors that can sum up to b (4): 12 and -8
(x + 12)(x - 8)
x = -12 and x = 8
Since -12 is not a possible width, x = 8 only.
Length = 12m and Width = 8m
Given: The length of the billboard is 4 m longer than its width
The area of the billboard = 96 m²
To find: The length and width of the billboard
Solution: Let the width of the billboard be x m.
Hence, the length of the billboard = (x + 4) m.
The area of a rectangle is given by length × breadth.
Therefore according to the question,
x(x + 4) = 96
⇒ x² + 4x = 96
⇒ x² + 4x - 96 = 0
⇒ x² - 8x + 12x - 96 = 0
⇒ x(x - 8) + 12(x - 8) = 0
⇒ (x - 8)(x + 12) = 0
Since the width cannot be negative, we will consider x = 8.
Therefore, the width of the billboard = 8 m.
The length of the billboard = (8 + 4) m = 12 m.
Answer: length = 12 m, width = 8 m