Question

The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.​

Answer 1

$\huge \sf \underline \red{Answer : }$

$\sf { \boxed{\underline{ \underline {\purple{ \tt{ \therefore \: Area = 480 \: }}}}}}$

$\huge \sf \underline \blue{Given : }$

• The diagonal of a rectangular plot is 34m and its perimeter is 92 m. find its area

$\huge \sf \underline \pink{To \: find : }$

• Area

$\huge \sf \underline \orange{solution : }$

• let length be a m
• breadth be b m

$\sf \underline{Given}$

• Diagonal is 34m
• perimeter is 92m

$\sf \underline{so}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{ {a}^{2} + {b}^{2} = ( {34)}^{2}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{ {a}^{2} + {b}^{2} = 1156}$

$\sf \underline{Again \: also : }$

• Given perimeter 92m

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{2(a + b) = 92}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{(a + b) = \dfrac{92}{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{(a + b) = 46}$

$\sf \underline{we \: know \: that \: area \: of \: rectangle = (ab) {m}^{2}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{( {46)}^{2} = 1156 + 2ab }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{ab = \dfrac{2116 - 1156}{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{ = \dfrac{960}{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⇢\sf{ = 480}$

$\sf \underline \purple{ \therefore \: Area = 480}$

Answer 2

Your Solution is in the attachment...