Question

Find the area of a rectangular plot whose one side is 48m and diagnol is 50m​

Answer 1

Answer:

length = 48cm = AB

In triangle DAB,

(DA)² + (AB)² = (DB)²

(DA)² + (48)² = (50)²

(DA)² = 2500-2304

(DA)² = 196

DA = 14 CM = Breadth

Now,

Area of rectangle = length × breadth

= 48 × 14 = 672 cm²

Answer 2

Given : Diagonal of the Rectangle is 50 m and of its side is 48 cm .

To Find : Find the Length of Rectangle

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

$\qquad \; {\green{\bigstar \; \; {\red{\underbrace{\underline{\purple{\sf{ {Diagonal}^{2} = {Length}^{2} + {Width}^{2} }}}}}}}}$

$\qquad \; {\green{\bigstar \; \; {\red{\underbrace{\underline{\purple{\sf{ Area = Length \times Width }}}}}}}}$

$\dag$ Calculating the Length :

${\longmapsto{\qquad{\sf{ { (Diagonal) }^{2} = { (Length) }^{2} + { (Width) }^{2} }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ { 50 }^{2} = { (Length) }^{2} + { 48 }^{2} }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 2500 = { (Length) }^{2} + 2304 }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 2500 - 2304 = {Length}^{2} }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \sqrt{2500 - 2304} = Length }}}} \\ \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \sqrt{196} = Length }}}} \\ \\ \\ \\ \ {\qquad \; \; {\longmapsto \; {\underline{\boxed{\pmb{\red{\frak{ Length = 14 \; m }}}}}}}} \; {\orange{\pmb{\bigstar}}}$

$\dag$ Calculating the Area :

${\dashrightarrow{\qquad{\sf{ Area = Length \times Width }}}} \\ \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area = 14 \times 48}}}} \\ \\ \\ \\ \ {\qquad \; \; {\dashrightarrow \; {\underline{\boxed{\pmb{\red{\frak{ Area = 672 \; {m}^{2} }}}}}}}} \; {\purple{\pmb{\bigstar}}}$

$\therefore \;$ Area of the Rectangle is 672 m² .

$\\ \qquad{\rule{200pt}{2pt}}$