Question

Find the premeter of the rectangle whose length 40 cm and a diagonal is 41 cm

Answer 1

41cm is the diagonal and 40cm is the length.

hyp² = length² + breadth²

41²   = 40² + breadth²

1681 = 1600 + breadth²

1681 - 1600 = breadth²

breadth² = 81

breadth = √81

= 9cm

Perimeter = 2( l + b )

              = 2 * (40 + 9)

              = 2 * 49

              = 98cm

The perimeter of the rectangle is 98cm.

Answer 2

Given:-

• Diagonal of the rectangle is 41 cm
• Length of rectangle is 40 cm.

To Find:-

• Perimeter of rectangle?

Solution:-

Breadth of rectangle:-

$\dag{ \boxed{ \underline{ \tt { \pink{hypotenuse² = length² + breadth²}}}}}$

$\Longrightarrow {41}^{2} = {40}^{2} + {b}^{2} \\ \\ \Longrightarrow 1681 = 1600 + {b}^{2} \\ \\ \Longrightarrow1681 - 1600 = {b}^{2} \\ \\ \Longrightarrow81 = {b}^{2} \\ \\ \Longrightarrow \sqrt{81} = b \\ \\ \Longrightarrow \dag{ \boxed{ \underline{ \tt{ \green{b = 9}}}}}$

Perimeter of rectangle:-

$\dag{ \boxed{ \underline{ \tt{ \blue{2 × (length+ breadth)}}}}}$

$\Longrightarrow 2(40 + 9) \\ \\ \Longrightarrow 2 × 49\\ \\ \Longrightarrow \dag{ \boxed { \underline{ \tt{ \red{98 cm}}}}}$

Hence, the Perimeter of rectangle is 98 cm.