Question

find the radius of a semicircle whose area is equal to half the sum of area of three semi circle whose radius r 3 4 and 5 cm

Answer 1

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$\huge \mathfrak {ANSWER:}$

GIVEN:
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• Area of a semicircle = 1\2 × ( π r1 ^2\2 + π r2 ^ 2\2 + π r3 ^2\2 ) ___ {1}

• r1 = 3 cm

• r2 = 4 cm

• r3 = 5 cm

We know that the area of a semicircle is 1\2 × π r^ 2 \2 ____{2}

Substitute all the radius in the equation {1}

• Area of a semicircle = 1\2 × ( π 9 \2 + π16\2 + π25\2 )

= 1\2 × ( 50π\2 )

= 25π\2 cm^2 _____ {3}

Now equate the equations {2} and {3}

1\2 πr^2 \2. = 25 π\2

r^2 \ 2 = 25

r^2 = 50

r = √50

r = 5 √2 cm

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