Question

the radius of a circle is less than twice the radius of other circle by 1 cm .The sum of their areas is 34πsqcm .Find the radius of each circle​

Answer 1

Answer:

|  Radius of first circle = 5 cm |

|  Radius of second circle= 3 cm |

Step-by-step explanation:

Let radius of 1st circle=$r$

Let radius of 2nd circle=$r`$

A.T.Q.

$r=2r`-1...............(i)\\=> r`= \frac{r+1}{2}$

Now, sum of area of circle=  $\pi r^{2}+ \pi r`^{2}=34\pi\\=>\pi(r^{2}+r`^{2})=34\pi\\=>r^{2}+r`{2}=34\\Now\;we\;know\;that\;r`=\frac{r+1}{2}.\;Now\;using\;this\;information,\\\\r^{2}+[\frac{r+1}{2}]^{2}=34\\=>r^{2}+[\frac{r^{2}+1+2r}{4}]=34\\=>4r^{2}+r^{2}+1+2r=136\\=>5r^{2}+2r-135=0$

Solving this quadratic equation as follows-

$5r^{2}+27r-25r-135=0\\=>r(5r+27)-5(5r+27)=0\\=>(r-5)(5r+27)=0\\=>r=5 \;\;or\;\; r=-27/5\\\\Since\;r\;is\;radius\;,\;hence\;r=5(because\;it\;can't\;be\;-ve)\\ Hence\;radius \;of\;first\;circle\;=5cm\\And\;radius\;of\;second\;circle=\frac{r+1}{2}=\frac{5+1}{2}=3$

$Learning\;\;together\;:)$