Can anyone please help me Two circles of radii 3cm and 4cm have the same total area as a third circle. What is the radius of the third circle.

5 cm

Step-by-step explanation:

Area of 3 cm circle

A = pi r^2 = pi *3^2 = 9pi

Area of 4 cm circle

A = pi r^2 = pi *4^2 = 16pi

The area of the new circle is 16pi+9pi = 25 pi

25 pi = pi r^2

Divide each side by pi

25 = r^2

Take the square root of each side

sqrt(25) = sqrt(r^2)

5 = r

The radius is 5

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584