Question

Calculati aria dreptunghiului cu laturile de:
A) (√3+3)cm si (√27+2) cm;
B) (5√5+1) cm si (√5-1) cm;
C) ( 6√3-3√2) cm si (6√3+ 3√2) cm;

Answer 1

$A = L \times l$

$A)A = ( \sqrt{3} + 3)( \sqrt{27} + 2)$

$A = ( \sqrt{3} + 3)(3 \sqrt{3} + 2)$

$A = 3 \sqrt{9} + 2 \sqrt{3} + 9 \sqrt{3} + 6$

$A = 3 \times 3 + 2 \sqrt{3} + 9 \sqrt{3} + 6$

$A = 9 + 11 \sqrt{3} + 6$

$A = (11 \sqrt{3} + 15) \: {cm}^{2}$

$B)A = (5 \sqrt{5} + 1)( \sqrt{5} - 1)$

$A = 5 \sqrt{25} - 5 \sqrt{5} + \sqrt{5} - 1$

$A = 5 \times 5 - 5 \sqrt{5} + \sqrt{5} - 1$

$A = 25 - 4 \sqrt{5} - 1$

$A = ( - 4 \sqrt{5} - 24) \: {cm}^{2}$

$C)A = (6 \sqrt{3} - 3 \sqrt{2} )(6 \sqrt{3} + 3 \sqrt{2} )$

$A = {(6 \sqrt{3}) }^{2} - {(3 \sqrt{2}) }^{2}$

$A = 108 - 18$

$A = 90 \: {cm}^{2}$