Question

question 4 (1 point) saved a rectangular garden measures 15 m long and 13.7 m wide. what is the length of a diagonal from one corner of the garden to the other? 18 m 19 m 2.0 x 10^1 m 4.1 x 10^2 m

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle (where the diagonal of the rectangle is the hypotenuse \(c\), and the length \(a = 15\) and width \(b=13.7\) are the other two sides) is \(c=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 15\) and \(b = 13.7\) into the formula: \(c=\sqrt{15^{2}+13.7^{2}}\).
First, calculate \(15^{2}=225\) and \(13.7^{2}=187.69\).
Then \(a^{2}+b^{2}=225 + 187.69=412.69\).

Step2: Calculate the square root

\(c=\sqrt{412.69}\approx20.31\).
\(20.31\approx2.0\times10^{1}\) (in scientific notation, where \(2.0\times10^{1}=20\)).

Answer:

\(2.0\times 10^{1}\text{ m}\) (the third option)