Answer:
[tex] \large \boxed{x + 5}[/tex]
Step-by-step explanation:
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[tex] \downarrow[/tex]
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{ \bold {\: (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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