Question

1. what is the length of a diagonal of rectangle efgh?

Explanation:

Step1: Identify side - lengths

Let's assume the horizontal side length (length of the rectangle) and vertical side length (width of the rectangle). By counting the grid - squares, if we assume each grid - square has a side - length of 1 unit. Let the length of the rectangle be $l$ and the width be $w$. From the graph, if we consider the horizontal side, the length $l$ (distance between two horizontal vertices) and the vertical side, the width $w$ (distance between two vertical vertices). Suppose the length of the rectangle is 10 units and the width is 4 units.

Step2: Apply the Pythagorean theorem

In a rectangle, the diagonal $d$ of a rectangle with length $l$ and width $w$ is given by the Pythagorean theorem $d=\sqrt{l^{2}+w^{2}}$. Substituting $l = 10$ and $w = 4$ into the formula, we get $d=\sqrt{10^{2}+4^{2}}=\sqrt{100 + 16}=\sqrt{116}=2\sqrt{29}\approx10.77$ units.

Answer:

$2\sqrt{29}$ units (or approximately 10.77 units if a decimal approximation is required)