Question

1. given a square with area x, you can use the formula (d = 1.4x^{\frac{1}{2}}) to estimate the length of the diagonal of the square. use the formula to estimate the length of the diagonal of a square with area 100 (cm^{2}).

Explanation:

Step1: Identify the value of x

The area of the square $x = 100\ cm^{2}$.

Step2: Substitute x into the formula

Substitute $x = 100$ into $d = 1.4x^{\frac{1}{2}}$. We get $d=1.4\times100^{\frac{1}{2}}$.
Since $100^{\frac{1}{2}}=\sqrt{100} = 10$, then $d = 1.4\times10$.

Step3: Calculate the value of d

$d=14\ cm$.

Answer:

$14\ cm$