Question

the area of rectangular carpet is 120 m square and the perimeter is 46 M find the length of the diagonals

Answer 1

Perimeter of rectangle = 2(l+b)
Given,
2(l+b)=46
=>(l+b) = 46/2 = 32cm.
=> l = (32 - b).

Area of rectangle = lb
Given,
$\: \: \: \: \: \: \: \: \: lb = 120 \\ = > (32 - b)b = 120 \\ = > 32b - {b}^{2} = 120 \\ = > {b}^{2} - 32b + 120 = 0 \\ = > {b}^{2} - 10b - 12b + 120 = 0 \\ = > b(b - 10) - 12(b - 10) = 0\\ = > (b - 10)(b - 12) = 0 \\ = > b = 10cm \: \: or \: \: 12cm.$

Both the answers are correct.
If b=10cm then l=12cm.
If l=10cm then b=12cm.

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