Question

Area of rectangle is 120 and its perimeter is 46 find lenght of diagonal

Answer 1

Area = l x b = 120

Perimeter = 2(l+b) = 46

so  ,  l + b = 23

l² + b² = ( l+b)² - 2 lb

      = 23² - 2 x 120 = 529 - 240 = 289

Diagonal = √l²+b² = √289 = 17

Answer 2

Area of rectangle =120

$l \times b = 120$
perimeter of rectangle =46
$2(l + b) = 46$
$l + b = 23$
so,we know that,,,

${(l + b)}^{2} = {(l - b)}^{2} - 4ab$
${23 }^{2} = {(l - b)}^{2} - 4 \times 120$
$529 + 480 = {(l - b)}^{2}$
$so.(l - b) = \sqrt{529 + 480} = \sqrt{1009}$
after solving equations (l+b) and (l-b) you will get the value of length and breadth.
with the help of l and b you can get diagonal.
from formula,..
$length \: of \: diagnal \: = \sqrt{ {l}^{2} + {b}^{2} }$
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