The area of square EFGH (not drawn to scale) is 144 $c m^{2}$ . Two squares, EPQR and GSTU, with sides 4 cm and 6 cm respectively are cut out as shown. Find the sum of lengths HR and FU.

10

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14

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20

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24

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Solution

The correct option is B $14$ cm
AREA OF SQUARE = A $= a^{2}$

The side length of EFGH $= {(a r e a)}^{1 / 2}$ $= {(144)}^{1 / 2}$ cm $= 12 c m$

$E H = 12 c m$

$R Q = Q P = P E = E R = 4 c m$ (sides of square RQPE)

$H R = H E - R E = (12 - 4) c m = 8 c m$

$T U = U G = G S = S T = 6 c m$

$F G = F U + U G = F U + 6 c m$

$F U = (12 - 6) c m = 6 c m$

$F U + H R = (6 + 8) c m = 14 c m$

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