Question

one side of a rectangular field is 15 m and one of its diagonal is 17m find the area of the field​

Answer 1

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First of all let's find other side in order to find its area !

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By Pythagoras theorem

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$\bold \red{(Side_1)^{2} + (Side_2) ^{2} = Diagonal ^{2} }$

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$\bold \pink{15^{2} + (Side_2) ^{2} = 17 ^{2} }$

$\bold \green{ (Side_2) ^{2} = 17 ^{2} - {15}^{2} }$

$\bold \pink{ (Side_2) ^{2} =64}$

$\boxed{ \bold \orange{ \leadsto \: (Side_2) =8}}$

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•°• Area of rectangle = 8 × 15 = 120 m²

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Answer 2

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Let the rectangle be ABCD

Let BC = 15 m

Diagonal AC = 17 m

AC = AB + BC

${AC}^{2} = {AB}^{2} + {BC}^{2}$

$AB = {√AC}^{2} - {BC}^{2}$

$AB = \sqrt{ {17}^{2} } - {15}^{2}$

AB = 8 m

Area of Rectangle = Length × Breadth

15 × 8 = 120

∴ Area of the Field = 120 m²