1.18: Length and area in a triangle

4PM1/2R/November/2020 — Question 3 · 8 marks

1.18 diagram 1
Figure 1 shows triangle ABC\displaystyle ABC in which AB=10 cm\displaystyle AB=10\,\mathrm{cm} and AC=12 cm\displaystyle AC=12\,\mathrm{cm}. The point D\displaystyle D lies on BC\displaystyle BC such that BD=6 cm\displaystyle BD=6\,\mathrm{cm}, DC=2 cm\displaystyle DC=2\,\mathrm{cm} and AD=x cm\displaystyle AD=x\,\mathrm{cm}.
(a) Show that x=11\displaystyle x=11.
(4)
(b) Find the area, in cm2\displaystyle \mathrm{cm}^2 to 3 significant figures, of triangle ADB\displaystyle ADB.
(4)