Question

(a) In figure (i) given below, AB = 12 cm, AC = 13 cm, CE = 10 cm and DE = 6 cm.
Calculate the length of BD.
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Answer 1

Given: AB = 12 cm, AC = 13 cm, CE = 10 cm and DE = 6 cm.

To find: Calculate the length of BD.

Solution:

• Consider triangle ABC, we get:

                AB² + BC² = AC²

                BC² = 13² - 12²

                BC² = 169 - 144

                BC² = 25

                BC = 5 cm

• In triangle EDC, we have:

                ED² + CD² = EC²

                CD² = EC² - ED²

                CD² = 10² - 6²

                CD² = 100 - 36

                CD² = 64

                CD = 8 cm

                CD + BC = 8 + 5

                BD = 13 cm

Answer:

           So the value of BC is 13 cm.