The figure is made from squares of different sizes. Find the area of A if the side of each of the two indentical smallest square is 2cm.

The area of square A is 256 cm²

Step-by-step explanation:

In the given figure

∵ The sides of the square E = 2 cm each

∵ The sides of the square F = 2 cm each

∵ The side of square D is the sum of the sides of squares E and F

∴ The sides of the square D = 2 + 2 = 4 cm each

∵ The side of square C is the sum of the sides of squares E and D

∴ The sides of square C = 2 + 4 = 6 cm each

∵ The side of square B is the sum of the sides of squares C, E, and F

∴ The sides of square B = 6 + 2 + 2= 10 cm each

∵ The side of square A is the sum of the sides of squares B, F, and D

∴ The sides of square A = 10 + 2 + 4= 16 cm each

∵ Area of square A = side × side

∴ Area of square A = 16 × 16

∴ Area of square A = 256 cm²

∴ The area of square A is 256 cm²

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

1. 34

2. 268

3. x=14.4

step-by-step explanation: