Question

The length of a rectangle is 16 cm and the length of its diagonal is 20 cm. Find the area of the rectangle​​

Answer 1

Answer:

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The Length, breadth and Diagonal of a rectangle form a right-angled triangle with the length and breadth as the perpendicular sides and the diagonal as the hypotenuse.

∴ diagonal² = length² + breadth² (by the Pythagorean theorem)

∴ 20² = 16² + b²

⇒ 20² - 16² = b²

⇒144 = b²

∴ b = √144 cm = 12 cm

Area of rectangle = length × breadth

= (16 × 12)cm²

= 192 cm²

Answer 2

$\bf{ \pmb{ \underline{ \gray{GIVEN}} }}\\ \cal \: Length \: of \: R ectangle \: is \: 16 cm \\ \cal \: Length \: of \: its \: Diagonal \: is \: 20 \: cm \\ \\ \bf { \pmb { \underline{ \gray{ To \: F ind }}}}\\ \large \: \blue{ \tt{ Area \: of \: Rectangle}} \\ \\ \huge \bf { \pmb{ \overline{\underline{ \color{black}{ \mid \: SOLUTION \: \mid}}}}} \\ \\ \large\tt{ \pmb{ \red{FORMULA \: \: \: USED}}} \\ \small \orange{\bf[\:{{(Diagonal)}^{2} = {(Length)}^{2} + {(Breadth)}^{2}}\:]} \\ \\ \sf{ \pmb{ CALCULATION }}\\ \rm \: (20)² = (16)² + (b)² \\ 400 = 257 + (b)² \\ 400 - 256 = (b)² \\ 144 = b² \\ \rm \: \sqrt{144 }= b \\ \rm \: 12 = b \\ \cal \blue{Thus, \: The \: Breadth \: of \: Rectangle \: is \: 12 \: cm . }\\ \\ \large\tt{ \pmb{ \red{ FORMULA \: \: \: USED}}} \\ \small \orange{ \bf[\:{Area \: of \: Rectangle =Length\times{Breadth}}\:] }\\ \\ \sf{ \pmb{CALCULATION }}\\ \rm Length × Breadth \\ 16 × 12 \\ 192 \\ \cal \blue{ Thus, \: The \: Area \: of \: Rectangle \: is \: 192 \: cm² }$