Question

find the perimetre and area of a rectangle one side of which measures 35m and diagonal 37m​

Answer 1

absolutely correct answer Umang Singh

Answer 2

$\tt{\green{ Length\: of\: first\: side( a ) = 35m }}$

$\tt{\green{ Length\: of\: second\: side( b ) = x }}$

$\tt{\green{ Length\: of\: diagonal( d ) = 37m }}$

$\tt{\green{ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: }}$

we know that d² = a² + b²

$\tt{\green{ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: }}$

$\tt{\red{ {d}^{2} = {a}^{2} + {b}^{2} }}$

$\tt{\red{\implies {37m}^{2} = {35m}^{2} + {b}^{2} }}$

$\tt{\red{\implies 1369 = 1225 +{ x}^{2}}}$

$\tt{\red{\implies 1369 - 1225m = {x}^{2}}}$

$\tt{\red{\implies 144m = {x}^{2}}}$

$\tt{\red{\implies \sqrt{144m} = x}}$

$\tt{\red{\implies 12 m= x}}$

$\tt{\green{ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: }}$

$\tt{\blue{ Area\: of\: rectangle = l × b}}$

$\tt{\blue{\implies Area\: of\: rectangle = 35m × 12m}}$

$\tt{\blue{\implies Area\: of\: rectangle = {420m}^{2}}}$

$\tt{\green{ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: }}$

$\tt{\orange{ perimeter\: of\: rectangle = 2 ( l + b ) }}$

$\tt{\orange{\implies perimeter\: of\: rectangle = 2( 35m + 12m)}}$

$\tt{\orange{\implies perimeter\: of\: rectangle = 2 × 47m}}$

$\tt{\orange{\implies perimeter\: of\: rectangle = 94m}}$