Question

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

Answer 1

see explanation

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 =
`√(225)` = 15 cm

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The area of Δ ABC is calculated as

A =
`(1)/(2)` × BC × AB =
`(1)/(2)` × 12 × 9 = 6 × 9 = 54 cm²