To find the diagonal distance across the square plaza, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the diagonal of the square plaza is the hypotenuse of a right triangle, and each side of the plaza is one of the other two sides. Given that each side of the plaza is 50 meters, we can label the sides of the right triangle as follows: - One side of the triangle is 50 meters (the length of one side of the plaza). - The other side of the triangle is also 50 meters (the length of another side of the plaza). - The diagonal distance across the plaza is the hypotenuse, which we'll call "d". Using the Pythagorean theorem, we can calculate the value of "d" as follows: d^2 = 50^2 + 50^2 d^2 = 2500 + 2500 d^2 = 5000 To find the value of "d", we need to take the square root of both sides of the equation: d = √5000 Calculating this value, we find that the diagonal distance across the plaza is approximately 70.7 meters (rounded to the nearest tenth). So, the diagonal distance across the plaza is approximately 70.7 meters.
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Answer:
70.7 m
Step-by-step explanation:
To solve the problem of finding the diagonal distance Elise walks across a square plaza, we'll use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
[tex]\boxed{ \begin{array}{ccc} \text{\underline{Pythagorean Theorem:}} \\\\ a^2 + b^2 = c^2 \\\\ \text{Where:} \\ \bullet \ a \ \text{and} \ b \ \text{are the lengths of the legs} \\ \bullet \ c \ \text{is the length of the hypotenuse} \end{array}}[/tex]
Given that 'a' and 'b' both equal 50 meters, we can plug this in to the equation above:
[tex]\Longrightarrow (50)^2+(50)^2=c^2\\\\\\\\\Longrightarrow 2500+2500=c^2\\\\\\\\\Longrightarrow 5000=c^2[/tex]
Now taking the square root of each side of the equation:
[tex]\Longrightarrow \sqrt{5000}=\sqrt{c^2}\\\\\\\\\Longrightarrow c= \sqrt{5000}\\\\\\\\\therefore c \approx \boxed{70.7 \text{ m}}[/tex]
Thus, the diagonal distance across the square plaza that Elise walks is approximately 70.7 meters, rounded to the nearest tenth of a meter.
