Geometry Test

OMTEX CLASSES “THE HOME OF SUCCESS”

1. Prove that the sum of the squares of the sides of a rectangle is equal to the sum of the squares of its diagonals. 2. Adjacent sides of a parallelogram are 11 cm and 17 cm. Its one diagonal is 26 cm. Find its other diagonal. 3. The walls of the buildings on opposite sides of a street are parallel to each other. A ladder 20 m long is placed so that its top just reaches the window of one building at the height 16 m. On turning the ladder over to the other side of the street, its top touches other building at the height 12m. Find the width of the street. 4. The ratio of the areas of two triangles, with equal heights is 2:3. Base of the larger triangle is 12 cm. Find the corresponding base of the smaller triangle. 5. In the map of a triangular field, sides are shown by 8cm, 7cm and 6 cm. If the largest side of the triangular field is 400 m, find the remaining sides of the field. 6. Find the diagonal of a square whose side is 20 cm. 7. Side of a rhombus is 10 cm, and one of its diagonals is 16 cm. Find the length of the other diagonal. 8. Areas of two similar triangles are 64 cm2 and 36 cm2. If one side of larger triangle is 12 cm, then find the corresponding side of smaller triangle. 9. Two triangles are similar and the ratio of their corresponding sides is 6:9. Area of smaller triangle is 48 sq. cm, then find area of larger triangle. 10.∆ ABC and ∆ DEF are equilateral triangles. A(∆ABC) : A(∆DEF) = 1:2 and AB = 4cm. Find DE.

OMTEX CLASSES “THE HOME OF SUCCESS” 1. The hypotenuse of a right angled triangle is 25 cm and the height is 7cm. Find the base of the triangle. 2. Side of an equilateral triangle is 8 cm. Find the side of an equilateral triangle whose area is twice the area of the first. 3. Find the diagonal of a rectangle whose sides are 20 cm and 15 cm. 4. In ∆ PQR, seg PM is a median. PM = 9 and PQ2 + PR2 = 290, then find QR. 5. Area of a rectangle is 192 sq. cm. and its length is 16 cm. Find the diagonal of the rectangle. 6. In a right angled triangle, hypotenuse is 61 cm and one side is 11 cm. Find its other side and area of the triangle. 7. Find the side of the square, whose diagonal is 16 cm. 8. In a right angled triangle, sides making right angle are 24 cm and 18 cm. Find its hypotenuse.

OMTEX CLASSES “THE HOME OF SUCCESS” 9. Find the diagonal of a square whose side is 20 cm. 10.Side of a rhombus is 10 cm, and one of its diagonals is 16 cm. Find the length of other diagonal.