Question

plz answer it correctly .......................​

Answer 1

Question :

Sum of the areas of two square is 850 m². If the difference of their perimeter is 40 m. Find the sides of the two squares.

AnsWer :

a= 25 m ,and b = 15 m.

Formula Use :

$\tt \red\star \: area \: of \: square = {(sides)}^{2} . \\ \tt \red\star \: perimeter \: of \: square = 4 \: sides.$

Explanation :

Let the area of first square be a and other be b.

Sum of area of two square is 840 m².

Calculation :

$\: \: \tt \: {a }^{2} +{ b }^{2} = 850. - - - (1) \\ \: \: \tt 4a - 4b = 40. \\ \tt \: \: \: \: \: \: \: a - b = \frac{ \cancel{40}}{ \cancel4} \\ \tt \: \: \: \: \: \: \: a - b = 10. - - - (2)$

Taking, equation (2), we get

$\tt \: \: a - b = 10. \\ \tt \: \: a = 10 + b. - - -( 3)$

Now, Putting the equation (3) in equation (1)

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt {a}^{2} + {b}^{2} = 850. \\ \tt \leadsto {(10 + b)}^{2} + {b}^{2} = 850.$

$\leadsto \tt 100 + {b}^{2} + 20b + {b}^{2} = 850. \\ \leadsto \tt2 {b}^{2} + 20b = 850 - 100.$

$\leadsto \tt2( {b}^{2} + 10b) = 750. \\ \leadsto \tt{b}^{2} + 10b = \frac{ \cancel{750}}{ \cancel2}$

$\leadsto \tt {b}^{2} + 10b = 375. \\ \leadsto \tt {b}^{2} + 10b - 375 = 0.$

$</p><p></p><p>\begin{array}{r | l}</p><p></p><p>5 & 375 \\</p><p></p><p>\cline{2-2} 5 & 75 \\</p><p></p><p>\cline{2-2} 5 & 15 \\</p><p></p><p>\cline{2-2} 3 & 3 \\</p><p></p><p>\cline{2-2} & 1 </p><p></p><p>\end{array}$

$\leadsto \tt {b}^{2} + 25b - 15b - 375. \\</p><p>\leadsto \tt b(b + 25)- 15(b + 25) = 0. \\ \leadsto \tt (b + 25)(b - 15) = 0.$

Either,

The value of b,

$\tt \leadsto b - 15 = 0. \: \: \: \: \: \: \: \: \: b + 25 = 0. \\ \: \: \: \: \: \: \: \: \tt \boxed{b = 15. \: \: \: and \: \: \: b = - 25.}$

$\: \: \boxed{b = - 25 \: {m} .} \\ \: \: \tt a = 10 + b. \\ \tt \: \: a = 10 - 25. \\ \tt \: \: a = - 15 \: {m} . \\ \tt or \\ \: \boxed{b = 15 \: {m} .} \\ \tt \: \: a = 10 + 15. \\ \tt \: \: a = 25 \: {m}.$

Area never be negative so, take positive,

Therefore, the value of side of square is a= 25 m and b= 15 m.