Question

the diagram shows a square piece of paper. jacob will cut along the dotted line to make two triangles of equal size.
7 cm
7 cm
what is the length of the dotted line?
a. $\frac{sqrt{7}}{2}$ cm
b. $sqrt{7}$ cm
c. $sqrt{14}$ cm
d. $7sqrt{2}$ cm

Explanation:

Step1: Identify the triangle type

The square has side length 7 cm. Cutting along the diagonal forms a right - triangle, where the two legs of the right - triangle are equal to the side length of the square (both 7 cm), and the dotted line is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Here, \(a = 7\) cm and \(b = 7\) cm. So we substitute these values into the formula:
\(c=\sqrt{7^{2}+7^{2}}=\sqrt{49 + 49}=\sqrt{98}\)
Simplify \(\sqrt{98}\): we can factor 98 as \(49\times2\), so \(\sqrt{98}=\sqrt{49\times2}=\sqrt{49}\times\sqrt{2}=7\sqrt{2}\) cm.

Answer:

D. \(7\sqrt{2}\) cm