Question : In triangle ABC, AD is the angle bisector of angle A. If AB = 8.4 cm, AC = 5.6 cm and DC = 2.8 cm, then the length of side BC will be:
Option 1: 4.2 cm
Option 2: 5.6 cm
Option 3: 7 cm
Option 4: 2.8 cm
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Correct Answer: 7 cm
Solution : The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle. So, $\frac{AB}{AC} = \frac{BD}{DC}$ ⇒ $\frac{8.4}{5.6} = \frac{BD}{2.8}$ ⇒ $\frac{8.4}{2} = BD$ ⇒ $4.2\mathrm{\ cm} = BD$ And, $BD + DC = BC$ ⇒ $BC = 4.2 + 2.8$ ⇒ $BC = 7\mathrm{\ cm}$ Hence, the correct answer is 7 cm.
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Question : In triangle ABC, the bisector of angle BAC cuts the side BC at D. If AB = 10 cm, and AC = 14 cm, then what is BD : DC?
Option 1: 10 : 7
Option 2: 5 : 7
Option 3: 7 : 5
Option 4: 7 : 10
Question : In triangle ABC, the bisector of angle BAC cuts the side BC at D. If AB = 10 cm, and AC = 14 cm then what is BD : BC ?
Option 1: 5 : 3
Option 2: 7 : 5
Option 3: 5 : 2
Option 4: 5 : 7
Question : ABC is a right angle triangle and $\angle ABC = 90^{\circ}$. BD is perpendicular on the side AC. What is the value of $(BD)^2$?
Option 1: $AD\times DC$
Option 2: $BC\times AB$
Option 3: $BC\times CD$
Option 4: $AD\times AC$
Question : Triangle ABC and DEF are similar. If AB = 92 cm, BC = 48 cm, AC =120 cm, and the length of the smallest side of triangle DEF is 200 cm, then find the length of the longest side of triangle DEF.
Option 1: 400 cm
Option 2: 225 cm
Option 3: 350 cm
Option 4: 500 cm
Question : Suppose $\triangle ABC$ be a right-angled triangle where $\angle A=90°$ and $AD\perp BC$. If the area of $\triangle ABC =40$ cm$^{2}$ and $\triangle ACD =10$ cm$^{2}$ and $\overline{AC}=9$ cm, then the length of $BC$ is:
Option 1: 12 cm
Option 2: 18 cm
Option 3: 4 cm
Option 4: 6 cm
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