ICSE Guess > ICSE/ISC eBooks > Class X > Maths by Mr. M. P. Keshari

ICSE / ISC eBooks

Exericise - 16

Q.1. On a map drawn to a scale of 1 : 25000, a rectangular plot of land, ABCD has the following measurements. AB = 12cm and BC = 16cm. Angle A, B, C, and D are all 90⁰ each. Calculate

1. The diagonal distance of the plot in km
2. The are of the plot in sq. km.

Q.2. The scale of map 1 : 2,00,000. A plot of land of area 25 km² is to be represented on the map. Find

1. The number of kilometers on the ground which is represented by 1 cm on the map
2. The area in km² that can be represented by 1 cm²
3. The area on the map that represents the plot of land.

Q.3. Draw a square ABCD with side 5 cm. Take any point O out side the square. Enlarge the square about O with a scale factor 2. What is the area of the image of the square?

Q.4. Construct a right angled triangle OAB with OA = 2cm, OB = 3cm and Enlarge the triangle about O with scale factor = 2 and its image What is the relation between the are of and its image

Q.5. A triangle with area 9cm² is enlarged with a scale factor 2. What is the area of its image?

Q.6. A square, whose area is 16cm², is transformed under enlargement about a point in the plane. If the area of the image is 64cm², find the scale factor of the enlargement.

Q.7. On a map drawn to a scale fo 1 : 2,50,000 a triangular plot of land had the following measurements, AB = 3cm, BC = 4cm,

1. The actual length of AB in km
2. Area of the plot in sq. km.

Q.8. A model of a ship is made to a scale of 1 : 200.

1. The length of the model is 5m.
   Calculate the length of the ship.
2. The area of the deck of the ship is 1,60,000m². Find the area of the deck of the model.
3. The volume of the model is 200 litres. Calculate the volume of the ship in m³.

Q.9. A model of a rectangular swimming pool was made to a scale of 1 : 500.

1. The length and width of the actual swimming pool are 100m and 50m respectively. Calculate the length and width on the model in cm.
2. If the model has the capacity to hold 240cm³ water, how much water can be stored in the actual swimming pool.

Q.10. The scale of a map is 1 : 5,00,000. A rectangular plot site of a company 5000m X 1,00,000m is to be represented on the map. Find

1. The number of cm on the map which would represent a distance of 20 km on the ground.
2. The area in cm² on the map which would represented the company plot.
3. The dimensions (in cm) on the map which would represented the factory plot.

Q.11. In a triangle ABC, DE is parallel to BC. If AE = 2cm, EC = 4cm and BC = 12cm, find the length of DE.

Q.12. In a triangle ABC, DE is parallel to BC. If AD = 4cm, DB = 2cm and the area of

1. Find the area of
2. 

Q.13. In the diagram along side,

1. Prove that are similar
2. If AC : BC = 3 : 2, find the ratio DE : AE.

Q.14. In the given diagram, are equilateral. D is the mid-point of BC and AP meets BC at Q. Prove that

1. 2PC = AB
2. BQ = 2CQ

Q.15. In the diagram alongside, DE is parallel to BC and Prove that

Q.16. Triangle ABC is right angled at A and AD is perpendicular to BC from A. If AB : AC = 11 : 5 find the ratio BD : DC.

Q.17. In Triangle ABC, BD and CE are perpendicular from B and C respectively to the opposite sides. Prove that

Q.18. In triangle ABC, AD is perpendicular from A to BC and respectively,

Q.19. In triangle ABC, DE is parallel to BC. If AD : DB = 2 : 3 and area of is 8cm², find the area of BCED.

Q.20. In the figure PQ RS is a parallelogram; PQ = 16cm; QR = 10cm, L is a point on PR such that RL : LP = 2 : 3, QL produced meets RS at M and PS produced at N.

1. Prove that triangles RLQ and PLN. are similar. Find the length of PN
2. Find a triangle similar to RLM. Evaluate RM.

Q.21. A line segment AB is divide at P in such a way that AB X BP = AP². BC is drawn perpendicular to AB and BC = AP. CQ is drawn perpendicular to AC to meet AB produced at Q. Prove that BP = BQ.

Q.22. ABC is a triangle with AC > AB. Line BD is drawn meeting AC at D such that Prove that BD² : BC² = AD : AC

Q.23. In triangle PQR, PB bisects and A is the mid-point of PQ. RC is parallel to PQ and meets AB produced at C. Find QB : BR in two different ways and show that PR = 2RC.

Q.24. In triangle is bisected by PX which meets QR in X. Y is a point in QR produced, such that PY = XY. Prove that are similar and show that XY is a mean proportional between QY and RY.

1. (i) 5km (ii) 12km2	2. (i) 2 km (ii) 4km2 (iii) 5cm2
3. 100 sq units	4.
5. 36m2	6. 2
7. (i) 7.5 km (ii) 37.5 sq. km	8. (i) 1000m (ii) 4m2 (iii) 16,00,000m3
9. (i) Length = 20cm, width = 10cm (ii)3,000m3	10. (i) 4cm (ii) 20cm2 (iii)1cm X 20cm
11. 4cm	12. 5(1/3)cm2 (ii) 4/5
13. 2 : 3	16.121 : 25
19. 42cm2	20. (i) 15cm (ii)