Question

Can any one help me please I need Complete information / details about the solution ​

Answer 1

`\huge \boxed{\mathbb{QUESTION} \downarrow}`

• Answer the 2 questions.

`\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}`

1st Question :-

a) State what's asked to find
`\downarrow`

• the length of the rectangular garden.

b) State the given facts
`\downarrow`

• area of a rectangular pool (garden) = x² + x - 12 cm²
• width of the garden = x + 4 cm.

c) Write a working equation
`\downarrow`

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
`\downarrow`

`\tt {x}^(2) + x - 12 = l * (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 (\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}}`

e) State your answer
`\downarrow`

• 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.

__________________

2nd Question :-

a) State what's asked to find
`\downarrow`

• the length of the side of the square.

b) State the given facts
`\downarrow`

• 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...

• x² + 10x + 25 = s × s

d) Solve the equation
`\downarrow`

`\tt {x}^(2) + 10x + 25 = s * s \\ \\ \sf \: s \: * \: 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}}`

e) State your answer
`\downarrow`

• The length of 1 side of the square is x + 5 cm.

__________________