The area of a square equals the square of a length of the side of the square. The perimeter of a square equals the sum of the lengths of all four sides. The sum of the areas of two squares is 65, while the difference in their areas is 33. Find the sum of their perimeters.

Accepted Solution

Answer:Step-by-step explanation:Let us take side of first square be aand other square side be LIt is given area of first square is equal to length of otheri.e. [tex]a^2=L[/tex]alsoSum of area of two square is 65 [tex]L^2+a^2=65[/tex]i.e. [tex]a^4+a^2=65----1[/tex]also Difference of area of two square is [tex]L^2-a^2=33[/tex][tex]a^2-a^2=33-----2[/tex]adding 1 and 2 we get[tex]2a^4=98[/tex][tex]a^4=49[/tex][tex]a^2=7[/tex]i.e. [tex]L=7[/tex]and [tex]a=\sqrt{7}[/tex]Perimeter of first Square[tex]P_1=4a=4\sqrt{7}[/tex][tex]P_2=4 L=4\times 7[/tex]Sum of Perimeter[tex]=4(\sqrt{7}+7) units[/tex]