[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
1st Question :-
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{ \bf \: (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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2nd Question :-
a) State what's asked to find [tex]\downarrow[/tex]
- the length of the side of the square.
b) State the given facts [tex]\downarrow[/tex]
- area of the tile = x² + 10x + 25 cm²
c) Write a working equation.
We know that, area of a square = side of the square × side of the square. Let's take the side of the tile (square) as 's'. So, the equation is...
d) Solve the equation [tex]\downarrow[/tex]
[tex] \tt {x}^{2} + 10x + 25 = s \times s \\ \\ \sf \: s \: \times \: s \: is \: equal \: to \: {s}^{2} \\ \\ \tt \: {x}^{2} + 10x + 25 = {s}^{2} \\ \\ \sf \: Using \: split \: the \: middle \: term \: method.. \\ \\ \tt \: {x}^{2} + 10x + 25 = {s}^{2} \\ \tt \: \left(x^{2}+5x\right)+\left(5x+25\right) = {s}^{2} \\ \tt x\left(x+5\right)+5\left(x+5\right) = {s}^{2} \\ \tt \: \left(x+5\right)\left(x+5\right) = {s}^{2} \\ \tt\left(x+5\right)^{2} = {s}^{2} \\ \\ \sf \: Now \: squaring \: on \: both \: the \: sides.. \\ \\ \tt \: \sqrt{(x + 5) ^{2} } = \sqrt{ {s}^{2} } \\ \large \boxed{\boxed{ \bf \: (x + 5) = s}}[/tex]
e) State your answer [tex]\downarrow[/tex]
- The length of 1 side of the square is x + 5 cm.
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