The floor of a rectangular living room is 5 meters by 8 meters. What is the distance between opposite corners of the living room? If necessary, round to the nearest tenth.
Understand the Problem
The question is asking for the distance between opposite corners of a rectangular living room, which can be calculated using the Pythagorean theorem. We will need to find the hypotenuse of a right triangle where the lengths are the sides of the rectangle.
Answer
The distance between the opposite corners is approximately $9.4$ meters.
Answer for screen readers
The distance between the opposite corners of the living room is approximately $9.4$ meters.
Steps to Solve
- Identify the sides of the rectangle
The lengths of the living room are given as 5 meters and 8 meters.
- Apply the Pythagorean theorem
To find the distance between the opposite corners (the hypotenuse ( c )), use the Pythagorean theorem: $$ c = \sqrt{a^2 + b^2} $$ where ( a = 5 ) meters and ( b = 8 ) meters.
- Calculate ( a^2 ) and ( b^2 )
Calculate the squares of the sides: $$ a^2 = 5^2 = 25 $$ $$ b^2 = 8^2 = 64 $$
- Add the squares
Now add these values together: $$ a^2 + b^2 = 25 + 64 = 89 $$
- Calculate the hypotenuse
Now take the square root to find the distance: $$ c = \sqrt{89} \approx 9.433981 \text{ meters} $$
- Round to the nearest tenth
Round ( 9.433981 ) to the nearest tenth: $$ c \approx 9.4 \text{ meters} $$
The distance between the opposite corners of the living room is approximately $9.4$ meters.
More Information
The Pythagorean theorem is a fundamental principle in geometry that relates the sides of a right triangle. It can be used in various applications, such as determining distances in real-life scenarios.
Tips
- Forgetting to round the final answer to the correct decimal place.
- Miscalculating the squares of the side lengths.
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