Answer:
4 inches long each i think im not completely sure
Step-by-step explanation:
Rectangle has its adjacent sides perpendicular to each other. The lengths of the sides of the considered rectangle are: 5 inches and 12 inches.
Its the sum of length of the sides used to made the given figure.
For a rectangle, as the rectangle has two of its sides equal to its length, and rest two are equal to its width, thus,
perimeter of rectangle = twice of (width + length)
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB.
In a rectangle, its adjacent sides are perpendicular to each other(making 90 degrees with each other), thus, when its diagonal is drawn, we can use Pythagoras theorem to relate its length, width and length of the diagonals (both of diagonals of a rectangle are of same length).
Thus, using Pythagoras theorem, we get:
[tex](|Diagonal|)^2 = |Length|^2 + |Width|^2[/tex]
Suppose its length and width are L and W, then we get two equations:
Perimeter = 2(L + W) = 34 inches
Diagonal² = 13² = 169 = L² + W²
From the first equation, getting L in terms of W, we get:
[tex]L = 17 - W[/tex]
Putting this value in second equation, we get:
[tex]L^2 + W^2 = 169\\(17-W)^2 + W^2 = 169\\289 + W^2 + W^2 -34W = 169\\2W^2 -34W + 120 = 0\\W^2 - 17W + 60 = 0\\W^2 -12W - 5W + 60 = 0 \\W(W - 12) - 5(W - 12) = 0\\\\(W-5)(W-12) = 0\\W = 5, 12[/tex](in inches)
Thus, we get L= 17-W = 12 or 5,
Thus, dimensions of the considered rectangle are 5 inches and 12 inches.
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