Question

Area of a rectangle is the same as the area of a square. If the rectangle is of measurement 25 in × 14 in, find the approximate (nearest tenth) length of each side of the square.

• A. 19.7 in
• B. 18.4 in
• C. 19.0 in
• D. 18.7 in

Answer 1

The correct option is D 18.7 in

$\text{Detailed step-by-step solution:}$
Length of the rectangle $=25$ in
Breadth of the rectangle $=14$ in
So, area of the rectangle $=25\times 14$ sq in
$=350$ sq in
Area of the rectangle $=$ Area of the square $=350$ sq in
Formula to find the area of a square $=a^2$, where a is the length of each side of the square.
According to the above formula,
$a^2=350$
$\Rightarrow \sqrt{a^2}=\sqrt{350}$ (taking square root on both the sides)
$\Rightarrow a=350$
We know that $324<350<361$.
$\Rightarrow \sqrt{324}<\sqrt{350}<\sqrt{361}$
$\Rightarrow 18<\sqrt{350}<19$
Trial and error method:
Considering the nearest tenth value:
$(18.5{)}^2=18.5\times 18.5=342.25(18.6{)}^2=18.6\times 18.6=345.96(18.7{)}^2=18.7\times 18.7=349.69(18.8{)}^2=18.8\times 18.8=353.44$
$350$ is closer to $349.69$ than $\mathrm{353.44.}$
That means $\sqrt{350}$ is closer to $18.7$ than $18.8$.
So, $\sqrt{350}\simeq 18.7$
$\Rightarrow a\simeq 18.7$ in

So, option C is the correct answer.