Question

the area of a rectangle is 65m2 ang the length is 3meter less than twice the width find the dimensions​

Answer 1

$\underline { \pink{ Dimensions \: of \: a\: rectangle : }}$

$Let \: width (w) = x\: m\: and$

$Length (l)\\ = (2 \times width - 3 )\: m \\= ( 2x - 3 ) \: m$

$Area\: of \: the \: rectangle = 65\: m^{2} \:(given)$

$\implies l \times w = 65$

$\implies ( 2x - 3 )\times x - 65 = 0$

$\implies 2x^{2} - 3x - 65 = 0$

/* Splitting the middle term, we get */

$\implies 2x^{2} - 13x + 10x - 65 = 0$

$\implies x( 2x - 13 ) + 5( 2x - 13 ) = 0$

$\implies ( 2x - 13 )( x + 5 ) = 0$

$\implies 2x - 13 = 0 \: Or \: x + 5 = 0$

$\implies 2x = 13 \: Or \: x = -5$

$\implies x = \frac{13}{2} \: Or \: x = -5$

/* x should not be negative . */

$\blue {x = \frac{13}{2}}$

Therefore.,

$\red{ Width } \green { = \frac{13}{2}}$

$\red{ Length } \\= (2x - 3 ) \\= 2 \times \frac{13}{2} - 3 \\= 13 - 3 \\\green {= 10 \: m }$

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Answer 2

Step-by-step explanation:

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