Question

The diagonals of square ABCD intersect at point E. If BE = 2x + 1, and AC = 3(6x-4), find BD.

Answer 1

Answer:

X=1

BD=AC=3(6x-4)=3(6(1)-4)=6

BD=6

Answer 2

Square is a polygon with 4 equal sides. The value of line BD is 6 units.

What is a square?

A square is a polygon with 4 sides, such that all the four sides of the polynomial are equal, also all the angles of the square are of 90°.

As it is given that the diagonals of square ABCD intersect at point E. And, we know that the diagonals of the square bisect each other. therefore, we can write,

BD = 2BE

Substituting the values, we will get,

$3(6x-4) = 2 \times(2x+1)\\\\18x-12 = 4x+2\\\\18x-4x = 2+12\\\\14x = 14\\\\x = \dfrac{14}{14}\\\\x = 1$

Thus, the value of x is 1.

We know that the diagonal of a square are equal, therefore, the value of the diagonal BD can be written as,

$BD = AC = 3(6x-4)$

Substitute the value of x as 1, therefore, the value of BD can be written as,

$BD = 3[6(1)-4]\\\\BD = 3(6-4)\\\\BD = 3 \times 2\\\\BD = 6$

Hence, the value of line BD is 6 units.

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