Question

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Answer 1

Answer: Using Pythagoras Theorem in triangle ABD

AD bisects BC therefore BD = 4.5 cm (star means multiplication)$\frac{1}{2} * AB * CE$

$AD^{2} + BD^{2} = AB^{2}$

$AD^{2} + 4.5^{2} = 7.5^{2}$

$AD^{2} = 7.5^{2} - 4.5^{2}$

$AD^{2} = (7.5+4.5)(7.5-4.5)$

$AD^{2} = (12)(3)$

$AD^{2} = 36$

$AD = \sqrt{36}$

$AD = 6cm$

Now area of triangle  

$\frac{1}{2} *BC*AD\\ =\frac{1}{2} * 9 * 6\\ =27 cm^{2}$

also the area of triangle : 1/2 * AB * CE = 27 (area of triangle remains same)

                                          1/2 * 7.5 * CE = 27

                                          CE = (27 * 2)(10)/75

                                          CE = 540/75

                                          CE = 7.2 cm

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