Question

the length of a square of side is 4 cm more than the length ofthe side of another square the sum of the areas of these two squares is 400 sq.cm. find the length of the side of each square

Answer 1

Answer:

the length of two squares is 12 and 16

Step-by-step explanation:

let the two squares is A and B

the side of square A = x

the side of square B = 4+x

area = side X side

so,

area of square A = side X side

= x X x

= x²

area of square B = side X side

=( 4+x) X (4+x)

= (4+x)² — [using identity (a+b)²]

= (4)²+(x)²+2X(4)(x)

=16 + x² + 8x

area of both squares A & B = 400

area of square A + area of square B = 400

x² + x² + 8x + 16 = 400

2x² + 8x + 16 - 400= 0

2x² + 8x -384 =0

solving this quadratic equation you get

x= 12 0r -16

side is not measured in Negative so the value of x is 12

and 4+ x= 4 + 12 = 16

so the side of square A = 12

& the side of square B = 16

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in this solution i am not solving quadratic equation ...you first solve then write ...

you can solve quadratic equation by

splitting the middle term or by quadratic formula

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quadratic formula

-b±√b²-4ac

2a