A rectangular closet has a perimeter of about 20 feet and a width of about 3 feet. Find the diagonal.
The perimeter P(=20 approx.) of a rectangle is twice the sum of width W(=3 approx.) and length L, or
P=2(W+L)
If W=3, then
20=2(3+L)
Solve for L to get L=7 (approximate, because W=3 is approximate)
The diagonal D can be found using Pythagoras theorem, namely
D=√(L²+W²)
Note that the answer is approximate because of the uncertainty of P and W.
Post your answer for a check if you wish.
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To find the diagonal of a rectangular closet, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 length and width of the closet form the legs of a right-angled triangle, and the diagonal is the hypotenuse. Let's denote the length of the closet as L, the width as W, and the diagonal as D.
Given that the perimeter of the closet is 20 feet, we can write the equation:
2L + 2W = 20
Since the width is given as 3 feet, we have:
2L + 2(3) = 20
2L + 6 = 20
2L = 20 - 6
2L = 14
L = 7
Now that we know the length of the closet is 7 feet and the width is 3 feet, we can use the Pythagorean theorem to find the diagonal:
D^2 = L^2 + W^2
D^2 = 7^2 + 3^2
D^2 = 49 + 9
D^2 = 58
To find the value of D, we need to take the square root of both sides:
D = √58
Therefore, the diagonal of the rectangular closet is approximately √58 feet.