Answered

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The length of a rectangle is 3m less than double the width, and the area of the rectangle is 65m^2 .
What is the length & width of the rectangle?

Sagot :

facundo3141592

By solving a quadratic equation, we will see that the length is 10m and the width is 6.5m

How to find the length and width of the rectangle?

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

A = W*L

In this case, we know that the area is 65m² and that the length is 3 meters less than 2 times the width, so:

L = 2*W - 3m

Then we can write:

65m² = (2*W - 3m)*W = 2*W² - 3m*W

This is a quadratic equation:

2*W² - 3m*W - 65m² = 0.

The solutions are given by the Bhaskara's formula:

[tex]W = \frac{3 \pm \sqrt{(-3)^2 - 4*2*(-65)} }{2*2} \\\\W = \frac{3 \pm 23 }{4}[/tex]

We only care for the positive solution, which is:

W = (3m + 23m)/4 = 26m/4 = 6.5m

Then the length is:

L = 2*6.5m - 3m = 10m

If you want to learn more about rectangles:

https://brainly.com/question/24571594

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