The point O is situated within the rectangular figure ABCD in such a way that OB = 6 cm., OD = 8cm. and OA = 5cm. Let us determine the length of OC.

A person goes 24m. west from a place and then he goes 10m. north. The distance of the person from starting point is

Two rods of 13m. length and 7m. length are situated perpendicularly on the ground and the distance between their foots is 8m. The distance between their top parts is

If ABC is an equilateral triangle and AD ⊥ BC, then AD² =

In ΔABC, if AB = (2a-1)cm. AC = 2 √2acm. And BC = (2a + 1)cm., then let us write the value of ∠BAC.

If the lengths of two diagonals of a rhombus are 24cm. and 10cm, the perimeter of the rhombus is

In the adjoining figure, the point O is situated within the triangle PQR in such a way that ∠POQ = 90°, OP = 6cm. and OQ = 8cm. If PR = 24cm. and ∠QPR = 90°, then let us write the length of QR.

I have drawn a triangle ABC whose height is AD. If AB>AC, let us prove that, AB²-AC = BD²-CD²

Let us fill in blanks:

(i) In a right angled triangle, the area of square drawn on the hypotenuse is equal to the _______of the areas of the squares drawn on other two sides.

(ii) In an isosceles right-angled triangle if the length of each of two equal sides is 42cm., then the length of the hypotenuse will be _______cm.

(iii) In a rectangular figure ABCD, the two diagonals AC and BD intersect each other at the point O, if AB = 12 cm., AO = 6.5 cm., then the length of BC is _______cm.

In ΔRST, ∠S is right angle. The mid- points of tow sides RS and ST are X and Y respectively; let us prove that, RY² + XT² = 5XY²

If the followings are the lengths of the three sides of a triangle, then let us write by calculating, the cases where the triangles are right-angled triangles:

9cm., 11cm. and 6cm.