Respuesta :
Answer: 20 meters
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Work Shown:
L = length
W = width
"ratio of length to width is 4:3", so L/W = 4/3
Let's solve for L
L/W = 4/3
3L = 4W .... cross multiply
L = 4W/3 ... we'll use this later in the next section
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P = perimeter of rectangle
P = 2*(L+W)
P = 2*(4W/3+W) ... replace L with 4W/3
P = 2*(4W/3+3W/3)
P = 2*(7W/3)
P = 14W/3
14W/3 = P
14W/3 = 56 ... plug in the given perimeter P = 56
14W = 56*3 ... multiply both sides by 3
14W = 168
W = 168/14 ... divide both sides by 14
W = 12
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Use that value of W to find L
L = 4W/3
L = 4*12/3
L = 48/3
L = 16
As a check, L/W = 16/12 = 4/3
also the four sides add up to 12+16+12+16 = 56 which is the given perimeter
so we have the proper length and width values
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Now we can find the diagonal. Note how a right triangle forms if you draw in one diagonal of the rectangle. The legs of the triangle are the length and width (L = 16, W = 12). The diagonal is the hypotenuse or longest side of the right triangle.
D = length of diagonal
D^2 = L^2+W^2 ... pythagorean theorem
D^2 = 16^2+12^2
D^2 = 256+144
D^2 = 400
D = sqrt(400) ... apply the square root to both sides
D = 20
