Question

If the total area of the land in the figure is 368 sq.m, then the correct values of the missing dimensions are

• A. A = 15 m, B = 7m
• B. A = 16 m, B = 8 m
• C. A = 17 m, B = 9 m
• D. A = 18 m, B = 10 m

Answer 1

The correct option is B A = 16 m, B = 8 m

The given figure is as follows:

The figure can be divided into two rectangles as:


Total area of the land is $368sq.m$

Hence,
Area of the $golden$ coloured rectangle $+$ Area of the $blue$ coloured rectangle $=$ $368sq.m$.

Now, for a rectangle, you know,
$Area=Length\times Breadth$.

So,
Area of the golden rectangle will be:
$=8m\times 8m=64sq.m$


∴ Area of blue rectangle
$=$ Total area $-$ Area of golden coloured rectangle
$=368sq.m-64sq.m$ $=304sq.m$

Using the formula for the area of a rectangle,
Area of blue rectangle = $Length\times Breadth=38m\times B$.

So, the breadth of the blue rectangle will be:
$B=\frac{304sq.m}{38m}=8m$

Side $A$ of the figure is $8m$ longer than the side $B$.

∴ The value of $A$ as $8m+8m=16m$.

∴ The correct values of the missing dimensions are:
$A=16m;B=8m$