If a square has an area of 4x^2−20x+25 square inches, what is the length of each side in inches?

Answer 1

square is: 4x^2−20x+25

side is: 2x-5

Please remember F-O-I-L and use Ax+B for each side.

Area of square = side squared = (Ax+B (Ax + B) = A²x + ABx + ABx + B² (remember F-O-I-L)

Now, the coefficients of each power of x (0, 1, and 2) must match, so:

A² = 4

2AB = -20

B² = 25

Thus, A=2. B=5

Now, get the signs of the numbers right:

s = side of square = (2x - 5)

Check this answer my squaring (2x-5) using F-O-I-L.

Answer 2

Given : Area of a square is 4x² - 20x + 25 square inches

To find the length of each side in inches

What do we know :

The 4 sides of a square are of equal length.

Area of the square = side × side

so ,we are finding the 2 identical factors of the given trinomial.

Since the given trinomial is a perfect square trinomial of the form A² - 2 AB +B², it can be factored as (A - B)(A - B).

That is, A²-2AB+B² = (A - B) (A - B) , where A - B is the length of each side of the square.

A =√ (4 x²) = 2x and B = √25 = 5

So, A - B = 2x -5

Answer; The length of each side is (2x - 5) sq.in.