Question

If the diagonal and the area of a rectangle are 25 m and 168 m2, what is the length of the rectangle?

Answer 1

this is answer ............

Answer 2

$Let \: l \:and \:b \: are \: length \:and \: breadth \\of \:a \: rectangle$

$Diagonal (d) = 25 \:m \: (given)$

$\implies \sqrt{l^{2} + b^{2}} = 25$

/* On squaring both sides,we get */

$\implies l^{2} + b^{2}= 625 \: --(1)$

$Area \: of \:the \: rectangle = 168 \:m^{2}$

$\implies l \times b = 168 \: ---(2)$

$\implies b = \frac{168}{l} \: ---(3)$

/*Subtract bothsides of equation (1) by 2lb , we get */

$\implies l^{2} + b^{2} - 2lb = 625 - 2lb$

$\implies ( l - b )^{2} = 625 - 2\times 168 \:[From \:(2) ]$

$\implies ( l - b )^{2} = 625 - 336$

$\implies ( l - b )^{2} = 289$

$\implies l - b = \pm \sqrt{17^{2}}$

$\implies l - b = 17\: --(4)$

$\implies l - \frac{168}{l} = 17\: [ From \:(3)]$

$\implies \frac{l^{2} - 168 }{l} = 17$

$\implies l^{2} - 17l - 168 = 0$

/* Splitting the middle term,we get */

$\implies l^{2} - 24l + 7l - 168 = 0$

$\implies l(l - 24) + 7( l - 24 ) = 0$

$\implies (l - 24)(l+7)= 0$

$\implies (l - 24) = 0 \: Or \: (l+7)= 0$

$\implies l = 24 \: Or \: l = -7$

/* But l should not be negative */

Therefore.,

$\red { Length \:of \:the \: rectangle } \green {= 24 \:m }$

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