Study the layout given in the figure and answer the question.

Write an expression for the total area covered by both the bedrooms and the kitchen?

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Solution

In bedroom 1 and bedroom 2,
Length $= x m$ ---(1)
Breadth $= 5 m$ ---(2)
In, Kitchen,
Breadth $= 5 m$ ---(3)
Since, length of the house is $15 m$ , length of bedroom is $x m$ and length of bath room is $2 m$ .
So, The length of the kitchen is $15 m - (x m + 2 m) = (13 - x) m$ ---(4)
Since, each shape of room is a Rectangle.
Area of the rectangle $=$ Length $\times$ Breadth
Now, Area of both bedrooms and the kitchen
$=$ (Area of bedroom) $\times 2 +$ Area of kitchen
$= (5 \times x) \times 2 + (13 - x) \times 5$ [Since, from (1), (2), (3) and (4)]
$= 10 x + (65 - 5 x)$
$= 10 x + 65 - 5 x$
$= (65 + 5 x)$
Therefore, Area of both bedrooms and the kitchen $(65 + 5 x) m^{2}$ .

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