Question

sum of the area of two square is 468m2. if the differences of their pweimeter is 24m ,find the sides of the two square. from quadratic equation.

Answer 1

Let the side of the larger square be x.

Let the side of the smaller square be y.

According to the question, x^2  + y^2 = 468 --------- (1)
Perimeters of the squares = 4x and 4y.
⇒ 4x - 4y = 24
⇒ x– y = 6
⇒ x= 6 + y
x^2  + y^2 = 468
Substituting the value of x in equation (1)
⇒ (6+y)^2 + y^2 = 468
⇒ 2y^2 + 12y + 36 = 468
⇒ y^2 + 6y + 18 = 234
⇒ y^2 + 6y - 216 = 0
⇒ (y – 12)(y + 18) = 0
⇒ y = 12 or -18

Since y denotes a length, it cannot be negative.
∴ y = 12
⇒ x = (12 + 6) = 18 m

∴ Sides of the squares are 18 m and 12 m.

hope it helps to you.

Answer 2

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