Question

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

• A. A = 15 ft ; B = 7 ft
• B. A = 16 ft ; B = 8 ft
• C. A = 17 ft ; B = 9 ft
• D. A = 18 ft; B = 10 ft

Answer 1

The correct option is B A = 16 ft ; B = 8 ft

The given figure is as follows:


The figure can be divided into two rectangles as such:


Total area of the land $=368sq.ft.$

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

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

So,
Area of the golden rectangle $=8ft\times 8ft=64sq.ft$.


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

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

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

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

∴ The value of $A$ as $8ft+8ft=16ft$.

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