Question

The sum of the areas of two circles is 80 pie square meters. Find the length of a radius of each circle if one of them is twice as long as the others

Answer 1

Answer:

The radius of the circles are $4\ m$  and   $8\ m$

Step-by-step explanation:

Let

x-----> the radius of larger circle

y----> the radius of smaller circle

we know that

$\pi x^{2} +\pi y^{2}=80\pi$

$x^{2} +y^{2}=80$ -----> equation A

Remember that

$x=2y$ -----> equation B

substitute equation B in equation A and solve for y

$(2y)^{2} +y^{2}=80$

$4y^{2} +y^{2}=80$

$5y^{2}=80$

$y^{2}=16$

$y=4\ m$

Find the value of x

$x=2y$

$x=2(4)=8\ m$

therefore

The radius of the circles are $4\ m$  and   $8\ m$