The length of Hannah's rectangular living room is 4 meters and the distance between opposite corners is 5 meters. What is the width of Hannah's living room? metersSubmit
Question
The length of Hannah's rectangular living room is 4 meters and the distance between opposite corners is 5 meters. What is the width of Hannah's living room? metersSubmit
Solution
To find the width of Hannah's living room, we can use the Pythagorean theorem because a rectangle's diagonal (the distance between opposite corners) and its width and length form a right triangle. The Pythagorean theorem states that the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides (the length and width of the rectangle).
In this case, the length of the diagonal is 5 meters and the length of the rectangle is 4 meters. Let's denote the width of the rectangle as w. According to the Pythagorean theorem, we have:
4^2 + w^2 = 5^2
Solving this equation for w gives:
w^2 = 5^2 - 4^2 w^2 = 25 - 16 w^2 = 9
Taking the square root of both sides gives:
w = 3
So, the width of Hannah's living room is 3 meters.
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