Question

Area of a square cardboard is $2.89sqft$. The length of the side of the cardboard is _____ ft and this length is ______________ number.

• A. $\mathrm{1.7...},$ an irrational
• B. $\mathrm{1.445....},$ an irrational
• C. $1.445,$ a rational
• D. $1.7,$ a rational

Answer 1

The correct option is D $1.7,$ a rational

Detailed step-by-step solution:
Area of the square cardboard $=2.89sqft$
Formula to find the area of a square $=a^2$ (if a is the length of sides)
So, $a^2=2.89$
$\Rightarrow a=\sqrt{2.89}$
$\Rightarrow a=\sqrt{1.7\times 1.7}$
$\Rightarrow a=1.7ft$
Here, $1.7$ is a terminating decimal number.
And a terminating decimal number is a rational number.
Hence, the length of the cardboard is a rational number.