Question

find the area of a rectangular plot, one side of which measures 35 m and the diagonal is 37 m.​

Answer 1

Step-by-step explanation:

Let ABCD be the rectangle

Length = 35m & Diagonal = 37m

Therefore, Breadth^2 = D^2 - L^2

Breadth^2 = 37m^2 - 35m^2

Breadth^2 = 1369m^2 - 1225m^2

Breadth^2 = 144m^2

Breadth = 12m

A/Q, Area = LxB

Area = 35mx12m

Area = 420 m^2

Answer 2

$\large{\underline{ \underline {\sf{\maltese \: {Given:-}}}}}$

• Side of the rectangular field = 35 m
• Diagonal of the rectangular field = 37 m

$\large{\underline{ \underline {\sf{\maltese \: {To \: find:-}}}}}$

• Area of the rectangular field = ?

$\large{\underline{ \underline {\sf{\maltese \: {Solution:-}}}}}$

Let ABCD be the rectangular plot.

$\quad \quad \sf{ \therefore{AB=35 \: m}} \\ \quad \quad \sf{ \therefore{AC=37\: m}}$

Let BC = (x) m

$\sf{From \: \triangle{ABC,} \: we \: have:}$

$\quad \quad \bull \: \bf{AC^2=AB^2+BC^2}$

$\qquad \quad {:} \longrightarrow \tt{ {37}^{2} = {35}^{2} + {x}^{2} }$

$\qquad \quad {:} \longrightarrow \tt{ {x}^{2} = {37}^{2} - {35}^{2} }$

$\qquad \quad {:} \longrightarrow \tt{ {x}^{2} = \bigg(37 + 35 \bigg)\bigg(37 - 35 \bigg) }$

$\qquad \quad {:} \longrightarrow \tt{ {x}^{2} = 72 \times 2 }$

$\qquad \quad {:} \longrightarrow \tt{ {x}^{2} = 144 }$

$\qquad \quad {:} \longrightarrow \tt{ {x} = \sqrt{144} }$

$\qquad \quad {:} \longrightarrow \tt{ {x} = 12}$

$\quad \sf{ \therefore \quad{BC=12 \: m}}$

$\quad \sf{ \therefore \quad{area \: of \: the \: plot = \bigg(35 \times 12 \bigg) {m}^{2} }} \\ \: \: \: \quad \qquad\qquad \qquad \sf{=420 {m}^{2} }$

$\large{\underline{ \underline {\sf{\maltese \: {Answer:-}}} }}$

• The area of the rectangular plot is 420 square metres