Question

find area of a rectangular plot is one side which is 48m and its diagonal is 50m. with full method​

Answer 1

Answer:

Area of the plot is 672m²

Explanation :

We know that,

Area of the rectangular plot = lenght × breadth.

To calculate the area we'll require it's breadth.

We have,

• Length = 48metres.
• Diagonal = 50metres.

By Pythagoras theorem,

→ diagonal² = length² + breadth²

→ 50² = 48² + b² [Taking ‘b’ as breadth]

→ 2500 = 2304 + b²

→ 2500 - 2304 = b²

→ 196 = b²

→ √196 = b

→ 14 = b

Therefore, the breadth of the plot is 14 metres.

So, tha area is

→ l × b

→ 48 × 14

→ 672m²

Required answer : 672m²

Answer 2

DIAGRAM :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,2.74){\framebox(0.25,0.25)}\put(4.74,0.01){\framebox(0.25,0.25)}\put(2,-0.7){\sf\large 48cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\qbezier(0,0)(0,0)(5,3)\put(1.65,1.8){\sf\large 50cm}\end{picture}$

$\:$

Given : One side of a rectangular plot is 48cm and it's diagonal is 50cm.

To Find : Area of the rectangular plot.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

Here

$\: \:$

• Length of the rectangular plot, AB = 48cm
• Diagonal of the rectangular plot, AC = 50cm
• Breadth of the rectangular plot, BC = ?

$\: \:$

As we know that :

$\:$

$\star\underline{\boxed{\sf\pink{AB {}^{2} + BC {}^{2} = AC {}^{2} }}} \:$

$\: \:$

$\sf:\implies \: AB {}^{2} + BC {}^{2} = AC {}^{2} \\ \\ \\ \sf:\implies \: (48) {}^{2} + BC {}^{2} = (50) {}^{2} \\ \\ \\ \sf:\implies \: BC {}^{2} = (50) {}^{2} - (48) {}^{2} \\ \\ \\\sf:\implies \: BC {}^{2} = 2500 - 2304 \\ \\ \\ \sf:\implies \: BC {}^{2} = 196 \\ \\ \\ \sf:\implies \: BC = \sqrt{196} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{BC = 14cm}}} \: \bigstar$

$\: \:$

$\sf\therefore{\underline{Hence, \: the \: breadth \: of \: the \: rectangular \: plot \: is \: \bold{14cm}.}}$

$\: \:$

We've got the breadth of the rectangular plot. Now we'll find the area of the rectangular plot.

$\: \:$

As we know that :

$\: \:$

$\star\underline{\boxed{\sf\pink{Area_{(rectangle)} = l \times b }}}$

$\: \:$

Where, l denotes length of the rectangle and b denotes breadth of the rectangle.

$\: \:$

$\sf:\implies \: Area_{(rectangle)} = l \times b \\ \\ \\ \sf:\implies \: Area_{(rectangle)} = 48 \times 14 \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{Area_{(rectangle)} = 672 {cm}^{2} }}} \: \bigstar$

$\:$

$\sf\therefore{\underline{Hence, \: the \: area \: of \: the \: rectangular \: plot \: is \: \bold{672cm {}^{2}}. }}$