A right triangle has one leg that measures 8 units and the other leg measures 6 units. Calculate the length of the hypotenuse.

6. ABCD is a quadrilateral, and AC and BD are its diagonals. Is \( \mathrm{AB}+\mathrm{BC}+\mathrm{CD}+\mathrm{DA}>\mathrm{AC}+\mathrm{BD} \) ? 7. ABCD is a quadrilateral and \( O \) is any point in its interior in the given figure Show that \( A B+B C+C D+D A<2(O A+O B+O C+O D) \).

9. ABC is a triangle in which \( \mathrm{m} \overline{\mathrm{BC}}=\mathrm{m} \overline{\mathrm{CA}}=2 \mathrm{~m} \overline{\mathrm{AB}} \). Internal bisector of \( \angle \mathrm{A} \) meets \( \overline{\mathrm{BC}} \) at D and \( \overline{\mathrm{DE}} \) is drawn parallel to \( \overline{\mathrm{CA}} \) meeting \( \overline{\mathrm{AB}} \) at E . Find \( \mathrm{m} \overline{\mathrm{DE}}: \mathrm{m} \overline{\mathrm{AB}} \).

111. The sum of the length, breadth and height of a cuboid is 38 cm and the length of its \( \vee \backslash \) diagonal is 22 cm . Find the surface area of the cuboid. Given : \( 1+b+h=38 \) and \( P^{2}+b^{2}+h^{2}=22^{2} \) To find : \( 2(l b+b h+h l) \)

In the figure below, the chord \( E F \) subtends angle of \( 114^{\circ} \) at the centre \( O \). Calculate (a) the length of the chord \( E F \),

Find equation of straight line through \( (-1,4) \) and perpendicular to the line passing through \( (3,0) \) and \( (1,-2) \).