If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, find the length of the sides of the rhombus.

4

(a)

For going to city B from city A, there is a route via city C such that \(AC\bot CB\) , AC = 2x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway, which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction on the highway?

4

(a)

Find the third side of a right angled triangle whose hypotenuse is of length p cm, one side of length q cm and p - q = 1.

4

(a)

Find the value of unknown variables, if \(\triangle ABC\) and \(\triangle PQR\)are similar.
      

4

(a)

In \(\triangle PQR\) and \(\triangle MST\) , \(\angle P={ 55 }^{ ° }\), \(\angle Q={ 25 }^{ ° }\), \(\angle M={ 100 }^{ ° }\) and \(\angle S={ 25 }^{ ° }\). Is \(\triangle QPR\sim \triangle TSM\) ? Why?

4

(a)

\(\triangle ABC\) and \(\triangle AMP\) are two right angled triangles. right angled at B and M, respectively. Prove that CA x MP = PA x BC

4

(a)

In the given figure, if \(\angle BAC\) = 90° and \(AD\bot BC\) . prove thart AD² = BD.CD

4

(a)

In the given figure, \(\angle M=\angle N=\) 46°. Express x in terms of a, b and c, where a, b and c are the lengths of LM, MN and NK respectively.

4

(a)

AD is an altitude of an equilateral \(\triangle ABC\) . In AD as base another equilateral triangle is ADE is constructed. Prove that \(ar\left( \triangle ADE \right) =ar\left( ABC \right) =3:4\) .

4

(a)

A ladder 17 m long, reaches at a window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.

4

(a)