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In ΔABC, ∠B = 90°, AB = 9 cm and BC = 12 cm. Calculate the length of AC. and area of triangle ABC ​

Respuesta :

Answer:

see explanation

Step-by-step explanation:

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AC² = AB² + BC² , substitute values

AC² = 9² + 12² = 81 + 144 = 225 ( take the square root of both sides )

AC = [tex]\sqrt{225}[/tex] = 15 cm

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The area of Δ ABC is calculated as

A = [tex]\frac{1}{2}[/tex] × BC × AB = [tex]\frac{1}{2}[/tex] × 12 × 9 = 6 × 9 = 54 cm²

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