On a map drawn to a scale of 1 : 250000, a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and ∠ABC = 90°. Calculate : (i) the actual length of AB in km. (ii) the area of the plot in sq. km.

(i) Since, the model of the triangular plot is made to the scale of 1 : 250000. ∴ K (Scale factor) = 250000. Actual length of AB = k × (the length of AB in model) = 250000 × 3 = 750000 cm. 1 cm = 10 -5 km. ∴ 750000 cm = 750000 × 10 -5 km = 7.5 km. Hence, the length of AB is 7.5 km. (ii) Since the plot is a right angled triangle. We know area of right angled triangle is given by Hence, area of the model is, We know that 1 cm 2 = 10 -10 km 2 . Hence, area of model = 6 × 10 -10 km 2 . Area of the actual plot = k 2 × (Area of the model) Putting values in above equation, Hence, the area of the plot is 37.5 km 2 .

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Two isosceles triangles have equal vertical angles and their areas are in the ratio 7 : 16. Find the ratio of their corresponding heights.

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On a map drawn to a scale of 1 : 50000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm. Find :
(i) the actual length of the diagonal AC of the plot in km.
(ii) the actual area of the plot in sq. km.

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ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC.
(i) Prove that △ADE ~ △ACB.
(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
(iii) Find, area of △ADE : area of quadrilateral BCED.

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Mathematics

On a map drawn to a scale of 1 : 250000, a triangular plot of land has the following measurements :
AB = 3 cm, BC = 4 cm and ∠ABC = 90°. Calculate :
(i) the actual length of AB in km.
(ii) the area of the plot in sq. km.

Similarity

Related Questions

Two isosceles triangles have equal vertical angles and their areas are in the ratio 7 : 16. Find the ratio of their corresponding heights.

On a map drawn to a scale of 1 : 50000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm. Find :
(i) the actual length of the diagonal AC of the plot in km.
(ii) the actual area of the plot in sq. km.

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC.
(i) Prove that △ADE ~ △ACB.
(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
(iii) Find, area of △ADE : area of quadrilateral BCED.

Mathematics

On a map drawn to a scale of 1 : 250000, a triangular plot of land has the following measurements :AB = 3 cm, BC = 4 cm and ∠ABC = 90°. Calculate :(i) the actual length of AB in km.(ii) the area of the plot in sq. km.

Similarity

Related Questions

Two isosceles triangles have equal vertical angles and their areas are in the ratio 7 : 16. Find the ratio of their corresponding heights.

On a map drawn to a scale of 1 : 50000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm. Find :(i) the actual length of the diagonal AC of the plot in km.(ii) the actual area of the plot in sq. km.

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC.(i) Prove that △ADE ~ △ACB.(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.(iii) Find, area of △ADE : area of quadrilateral BCED.

On a map drawn to a scale of 1 : 250000, a triangular plot of land has the following measurements :
AB = 3 cm, BC = 4 cm and ∠ABC = 90°. Calculate :
(i) the actual length of AB in km.
(ii) the area of the plot in sq. km.

On a map drawn to a scale of 1 : 50000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm. Find :
(i) the actual length of the diagonal AC of the plot in km.
(ii) the actual area of the plot in sq. km.

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC.
(i) Prove that △ADE ~ △ACB.
(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
(iii) Find, area of △ADE : area of quadrilateral BCED.