Question

Mrs. Reyna is planning to fence her
vacant lot for a parking space. The
desired length of the lot is 6 meters
longer than its width. What will be
the possible dimensions of the
rectangular parking space if it
should be less than 40sqm? (Hint:
length x width = Area of rectangle)

giving 10 pts​

Answer 1

$\sf \huge \purple{Answer - }$

Possible dimensions,

Width = (0 , 4) or length - 6

Length = (6 , 10) or width + 6

Step-by-step explanation:

Let, width = x

length = x + 6

area < 40 m²

Solve,

Area = Length x Width

40 > (x + 6) x

40 > x² + 6x

0 > x² + 6x - 40

Rearrange and Factor,

(x + 10) (x - 4) < 0

Solve the inequalities,

$\longrightarrow$ x + 10 < 0

$\longrightarrow$ x1 < -10

$\longrightarrow$ x - 4 < 0

$\longrightarrow$ x2 < 4

Therefore, x (-10 , 4) = width

Length = x + 6

length = ( -4 , 10)

Since we're dealing with measurements, we disregard the negative values.

Width = (0 , 4)

Length = (6 , 10)