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Chapter 11: Q. 81 (page 774)

Two circles have circumferences that add up to 12蟺cmand areas that add up to 20蟺cm2. Find the radius of each circle.

Short Answer

Expert verified

The radius of the two circles are 2and4.

Step by step solution

01

Step 1. Given information.

Assume x to be the radius of the first circle and y to be the radius of the second circle.

From the question,

2蟺虫+2蟺测=12蟺......(i)蟺虫2+蟺测2=20蟺......(ii)

Take out the common factors from equation (i),

2蟺x+y=2蟺6x+y=6.......(iii)

Take out the common factors from equation (ii),

蟺x2+y2=20蟺x2+y2=20......(iv)

02

Step 2. Solve equation (iii) for x.

Solving equation (iii) for x,

x=6-y

Substitute the value of x in equation (iv),

localid="1646849857123" role="math" 6-y2+y2=20y-4y-2=0y=4,2

Substitute y=4in equation (iii),

x+4=6x=2

Substitute y=2in equation (iii),

x+2=6x=4

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