The perimeter of a rectangle is 42m and its diagonal is 15m.what are the lengths of its sides
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Given, 2(L+B) = 42m
=> (L+B) = 42/2
L+B= 21 m____________(1)
and diagonal = 15m
By pythagorus theorem
L² + B² = 15²
L² + B² + 2LB - 2LB = 225
(L+B )²- 2LB = 225
21² - 2LB = 225
441 - 2LB = 225
2LB = 441-225
2LB = 216
LB = 108
L = 108/B____(2)
substitute (2) in (1)
108/B + B = 21
multiplying the whole equation with B
(108/B + B = 21)B
=> 108×B/B + B×B = 21×B
=> 108 + B² = 21B
=> B² -21B +108 = 0
=> B² -12B -9B + 108 = 0
=> B (B-12) -9 (B-9)
=> (B-12) (B-9)
=> B=12 OR B=9
if B = 12m , L= 9m _________(From (1))
if B = 9m, L = 12m __________(From (1))
So, the side lengths are 9m and 12m
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