Quadrilateral abcd is a square and the length of be is 6cm what is the length of ac

8.5cm or √72 cm

Step-by-step explanation:

Line AC is a diagonal of the square ABCD.

All squares have four equal sides, so we know all sides are 6 cm.

Imagine the square cut in half diagonally to make two triangles. You can use the Pythagorean theorem because squares have all right angles.

The Pythagorean formula is used for right-angle triangles to find side lengths.

The formula is a² + b² = c², where "a" and "b" are the base and height, "c" is the hypotenuse, which is the longest side of the triangle.

Line AC is the hypotenuse. The base and height are two other sides of the triangle, which are 6cm.

Use the formula and substitute the side lengths to find the hypotenuse, "c".

a² + b² = c²

(6cm) ² + (6cm) ² = c²

36cm² + 36cm² = c² Simplify by adding

72cm² = c² Square root both sides to isolate c

√ (72cm²) = c

c = √ (72) cm Simplified the units. Exact answer for AC

c ≈ 8.5cm Rounded to one decimal place

Therefore AC is about 8.5cm.