Given: ABCD is a rectangle,
AB = 9 cm, BC =? 3 cm> AB.
Find: AC =? cm
1) BC = 9 + 3 = 12 cm.
2) the diagonal AC forms with the sides of the rectangle AB and BC a right-angled triangle ABC, in which AB and BC are the legs, AC is the hypotenuse.
By the theorem, the square of the hypotenuse is equal to the sum of the squares of the legs: AC ^ 2 = AB ^ 2 + BC ^ 2.
Substitute the data: AC ^ 2 = 9 ^ 2 + 12 ^ 2,
AC ^ 2 = 81 + 144 = 225,
AC = root of 225 = 25 cm.
Answer: AC = 25 cm.
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