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The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 10 cm, and its area is 12 cm2. Find the radius of the inscribed circle.

Respuesta :

frika

Answer:

1.2 cm

Step-by-step explanation:

The area of sircumscribed quadrilateral over a circle is equal to

[tex]A=s\cdot r,[/tex]

where s is semi-perimeter of the quadrilateral and r is the radius of the circle.

Use property of circumscribed quadrilateral: The sums of the opposite sides are equal.  

So, if the sum of two opposite sides of the circumscribed quadrilateral is 10 cm, then the sum of another two sides is also 10 cm and the perimeter of the quadrilateral is 20 cm. Hence,

[tex]s=\dfrac{20}{2}=10\ cm[/tex]

Now,

[tex]A=s\cdot r\\ \\12=10r\\ \\r=\dfrac{12}{10}=1.2\ cm[/tex]

facundo3141592

We will see that the radius of the inscribed circle is 1.2 cm.

How to get the radius?

Remember that for a rectangle of length L and width W, the area is:

A = L*W

In this case we know that the sum of two opposite sides is 10cm, then we can have:

2*L = 10cm

L = 10cm/2 = 5cm

And the area is 12 cm, so we can solve:

12cm = 5cm*W

12cm/5cm = W = 2.4cm

Now, the circle must be inside of the rectangle, so its diameter is equal to the smaller side of the rectangle, which is 2.4cm

Then we have:

D = 2.4cm

And the radius is half of the diameter, so the radius is:

R = 2.4cm/2 = 1.2 cm

If you want to learn more about circles, you can read:

https://brainly.com/question/1559324

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