The AC diagonal divides the ABCD rectangle into two right-angled triangles – ABC and BCD, where AC is their common hypotenuse. We find the hypotenuse by the Pythagorean theorem:
AC² = AB² + BC²;
AC = √ (AB² + BC²).
Find the side of the rectangle BC if the perimeter is 14 cm:
2 * 3 + 2 * BC = 14;
2 * BC = 8;
BC = 4 cm.
Let’s find the hypotenuse, it is also the diagonal of the rectangle:
AC = √ (3² + 4²);
AC = √25;
AC = 5 cm.
Answer: The length of the AC diagonal is 5 cm.
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