Answered

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3. The diagonal of a rectangular field is 169 m. Ifthe ratio of the length to the width is 12:5, find the: (a) (b) dimensions; perimeter of the field.​

Sagot :

facundo3141592

The dimensions of the rectangle are length 156 m and a width of 65m, and a perimeter P = 442m

How to find the dimensions of the rectangle?

For a rectangle of length L and width W, the diagonal is:

[tex]D = \sqrt{L^2 + W^2}[/tex]

Here we know that the diagonal is 169m.

And the ratio of the length to the width is 12:5

This means that:

W = (5/12)*L

Replacing all that in the diagonal equation:

[tex]169 = \sqrt{((5/12)^2*L^2 + L^2} \\\\169^2 = (25/144)*L^2 + L^2 = ( 25/144 + 1)*L^2\\\\\frac{169}{\sqrt{25/144 + 1} } = L = 156[/tex]

So the length is 156 meters, and the width is:

W = (5/12)*156 m = 65m

Finally, the perimeter is:

P = 2*(L + W) = 2*(156 m + 65m) = 442m

If you want to learn more about rectangles:

https://brainly.com/question/17297081

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