A rectangular carpet has an area of 120 , m^{ | vedclass

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(C) Let the length be $a \, m$ and the breadth be $b \, m$.The perimeter of a rectangle is given by $2(a + b) = 46 \, m$.Therefore,$a + b = 23 \, m$.T

Vedclass · Accepted Answer

$17$

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(C) Let the length be $a \, m$ and the breadth be $b \, m$.The perimeter of a rectangle is given by $2(a + b) = 46 \, m$.Therefore,$a + b = 23 \, m$.The area of the rectangle is given by $a 	imes b = 120 \, m^{2}$.The length of the diagonal $d$ is given by the formula $d = \sqrt{a^{2} + b^{2}}$.Using the algebraic identity $(a + b)^{2} = a^{2} + b^{2} + 2ab$,we can write $a^{2} + b^{2} = (a + b)^{2} - 2ab$.Substituting the known values: $a^{2} + b^{2} = (23)^{2} - 2(120) = 529 - 240 = 289$.Thus,the diagonal $d = \sqrt{289} = 17 \, m$.

$A$ rectangular carpet has an area of $120 \, m^{2}$ and a perimeter of $46 \, m$. The length of its diagonal is ...... $m$.

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