Question

the diagram below shows the dimensions of a rectangular field. what is the length of a diagonal of the field? 120 ft. 200 ft. 394 ft. 520 ft.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle (a rectangle's diagonal divides it into two right - triangles), if the sides of the right - triangle are \(a\) and \(b\), and the hypotenuse is \(c\), then \(c^{2}=a^{2}+b^{2}\). In a rectangle with length \(l = 160\) ft and width \(w = 120\) ft, the diagonal \(d\) is the hypotenuse of a right - triangle with legs 120 ft and 160 ft.

Step2: Substitute values into the formula

Let \(a = 120\) and \(b=160\). Then \(d^{2}=120^{2}+160^{2}\). Calculate \(120^{2}=120\times120 = 14400\) and \(160^{2}=160\times160=25600\). So \(d^{2}=14400 + 25600=40000\).

Step3: Find the square - root

Take the square - root of both sides to find \(d\). Since \(d^{2}=40000\), then \(d=\sqrt{40000}=200\) ft.

Answer:

200 ft