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the perimeters of a square and rectangle are equal. one side of a rectangle is 11cm and the area of the square is 4cm^2 more than the area of the rectangle. find the side of the square.

Sagot :

Answer:

The side of the square can be 13 or 9

Step-by-step explanation:

Let x equal the unknown side of the rectangle and y equal the side of the square. The given information is that the area of the square is 4cm^2 larger than that of the rectangle. Mathematically this can be represented as

[tex]11x+4=y^2[/tex]

The second known is that their perimeters are equal so,

[tex]22+2x=4y[/tex]

Solve the first equation in terms of x and substitute it into the second and you get the quadratic

[tex]y^2-22y+117=0[/tex]

[tex](y-13)(y-9)=0[/tex]

Therefore your side length for the square can be either of those.

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