Triangles Set-2

Q1. In right triangle ABC with right angle at B, the hypotenuse $AC=13\text{ cm}$ and one leg $AB=5\text{ cm}$. Find the length of $BC$.

Q2. In right triangle ABC with right angle at B, the altitude from B meets hypotenuse AC at D. If $AD=9\text{ cm}$ and $DC=16\text{ cm}$, then the lengths $AB$ and $BC$ are respectively:

Q3. The external bisector of $\angle A$ of $\triangle ABC$ meets the extension of $BC$ at $D$. Given $AB=6\text{ cm}$, $AC=8\text{ cm}$ and $BD=4\text{ cm}$, find $DC$.

Q4. In $\triangle ABC$, $AB=13\text{ cm}$, $AC=15\text{ cm}$ and the median from $A$ has length $14\text{ cm}$. Find the length of $BC$.

Q5. In $\triangle ABC$, sides are $AB=13\text{ cm}$, $BC=14\text{ cm}$ and $CA=15\text{ cm}$. The median from $A$ to side $BC$ has length:

Q6. In right-angled triangle ABC with $\angle C=90^\circ$, the altitude from $C$ meets the hypotenuse $AB$ at $D$. If $AD=4$ and $DB=9$, then the length of $AC$ is

Q7. In $\triangle ABC$, a line through $P$ on $AB$ is drawn parallel to $BC$ and meets $AC$ at $Q$. If $AP=4,\;PB=8$ and $AC=18$, then $AQ$ equals

Q8. In $\triangle ABC$, the median from $A$ has length $13$, and $AB=10,\;AC=17$. The length of $BC$ is

Q9. For all triangles with fixed base $BC=10$ and fixed sum $AB+AC=18$, the maximum possible area of $\triangle ABC$ is

Q10. A triangle has side lengths $13,\;14,\;15$. The length of the altitude to the side of length $14$ is

Q11. In triangle $ABC$, $\angle B=90^\circ$, $AB=12\ \text{cm}$ and $BC=5\ \text{cm}$. Find the length of $AC$.

Q12. In right triangle $ABC$ with $\angle C=90^\circ$, the altitude from $C$ meets the hypotenuse $AB$ at $D$. If $CD=6\ \text{cm}$ and $AD=9\ \text{cm}$, then the length of $AC$ is

Q13. In triangle $ABC$, $AB=10\ \text{cm}$ and $AC=8\ \text{cm}$. The internal bisector of $\angle A$ meets $BC$ at $D$. If area$(\triangle ABD)=20\ \text{cm}^2$, then area$(\triangle ADC)$ equals

Q14. Let $B(0,0)$ and $C(6,0)$. Point $A$ has coordinates $(k,h)$ (with $h\neq 0$). If the medians from $B$ and $C$ are equal in length, the $x$-coordinate $k$ of $A$ is

Q15. If the three sides of a right-angled triangle are in arithmetic progression, then their ratio must be