Question

If the perimeter of a rectangle plot is 68 m and length of its diagonal is 26m, find its area

Answer 1

$here \: is \: your \: answer$

Perimeter = P = 2L + 2W = 68

so L + W = 34, or

W = 34 - L.

↪The diagonal is 26, and so by the Pythagorean Theorem, 

${l}^{2} + {w}^{2} = {26}^{2}$

↪By direct substituion,⤵

${l}^{2} + (34 - l {)}^{2} = 676$

${l}^{2} + 1156 - 68L + {l}^{2} = 676$

L²+68L +480 =0

L² + 34L+ 240 =0

(L² -24 )*(L - 10 ) = 0

↪This means L = 24, or L =10.

Since ,

↪we usually take the longer value value to be the length, L = 24, and from this W = 10.

$hope \: it \: helps$

$\beta e \: \beta \gamma \alpha inly$

Answer 2

Perimeter = P = 2L + 2W = 68

so L + W = 34, or

W = 34 - L.

↪The diagonal is 26, and so by the Pythagorean Theorem,

{l}^{2} + {w}^{2} = {26}^{2}l

2

+w

2

=26

2

↪By direct substituion,⤵

{l}^{2} + (34 - l {)}^{2} = 676l

2

+(34−l)

2

=676

{l}^{2} + 1156 - 68L + {l}^{2} = 676l

2

+1156−68L+l

2

=676

L²+68L +480 =0

L² + 34L+ 240 =0

(L² -24 )*(L - 10 ) = 0

↪This means L = 24, or L =10.

Since ,

↪we usually take the longer value value to be the length, L = 24, and from this W = 10.