SSC MTS Model Paper 2

Question : 41 of 150

Marks: +1, -0

The area of the square with AC as a side is 128 cm

^2

. What is the sum of the areas of semicircles drawn on AB and AC as diameters, given ABC is an isoscles right angled triangle and AC is its hypotenuse.

32π cm $^2$
16π cm $^2$
16 cm $^2$
32 cm $^2$

Validate

Solution:

(2)

Let

A B = B C = x

then

A C = √ { 2 } x

But

A C = √ { 128 } = 8 √ { 2 } { cm }

√ { 2 } x = 8 √ { 2 } x = 8 { cm }

Areas of semicircles

= { 1 } /{ 2 } π ( { x } /{ 2 } ) ^ { 2 } + { 1 }/ { 2 } π ( { x }/ { 2 } ) ^ { 2 }

= { 1 }/ { 2 } π ( 2 × 16 ) = 16 π { cm } ^ { 2 }

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