Question

Find the length of a perimeter of the re tangle of whose length is 40 cm and a diagonal is 41cm

Answer 1

Answer:

The diagonal of the rectangle divides it into two right-angled triangles, so we can use the pythagorean theorem to solve this problem. 

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

Step-by-step explanation:

the length of the rectangle - 40 cm

its diagonal - 41 cm

so, according to Pythagorean theorem:-

$( {h}^{2} ) = ( {p}^{2} ) + ( {b}^{2} )$

so,

$( {b}^{2} ) = ( {h}^{2} ) - ( {p}^{2} )$

${b}^{2} = {41}^{2} - {40}^{2}$

${b}^{2} = 1681 - 1600$

${b}^{2} = 81$

$b = \sqrt{81}$

$b = 9cm$

the perimeter of the rectangle :-

$2(l + b)$

$= 2(40 + 9)$

$= 80 + 18$

$= 98 \: cm$

so that, the perimeter will be 98 cm....

I hope it will help you...!