Answer:
[tex] \large \boxed{x - 3}[/tex]
Step-by-step explanation:
a) State what's asked to find [tex] \downarrow[/tex]
- The length of the rectangular garden.
b) State the given facts [tex] \downarrow[/tex]
- Area of a rectangular pool (garden) = x² + x - 12 cm²
- Width of the garden = x + 4 cm
c) Write a working equation [tex] \downarrow[/tex]
Area of the garden = length of the garden × width of the garden. Let's take the length as 'l'. So the equation is...
- x² + x - 12 = l × (x + 4)
d) Solve the equation [tex] \downarrow[/tex]
[tex]\tt {x}^{2} + x - 12 = l \times (x + 4) \\ \\ \sf \: Bring \: (x + 4) \: towards \: the \: left \: side \\ \sf\: of \: the \: equation. \\ \\ \tt \frac{ {x}^{2} + x - 12 }{x + 4} = l \\ \\ \sf \: Factor \: the \: expressions \: that \: are \\ \sf \: not \: already \: factored. \\ \\ \tt \frac{\left(x-3\right)\left(x+4\right)}{(x+4)} = l\\ \\ \sf Cancel \: out \: (x + 4) \: in \: both \: the \\ \sf \: numerator \: and \: denominator. \\ \\ \large \boxed{\boxed{ \bold{\: (x-3 )= l}}}[/tex]
e) State your answer [tex] \downarrow[/tex]
The length of the rectangular garden is x - 3 cm.
Note :-
I think there's a mistake in the question. It should be the area of the rectangular garden & not area of the rectangular pool because here we are asked to measure the length of the garden.
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