Problems on Size Transformation

Here we will solve different types of problems on size transformation.

1. A map of a rectangular park is drawn to a scale of 1 : 5000.

(i) Find the actual length of the park if the length of the same in the map is 25 cm.

(ii) If the actual width of the park is 1 km, find its width in the map.

Solution:

(i) Given scale = 1 : 5000

Let the actual length of the park be p

Therefore, Length in MapActual Length of the Park = 15000

25cmp = 15000

⟹ p = 25 × 5000 cm

⟹ p = 125000 cm

⟹ p = 125000 × 105 km

⟹ p = 1.25 km


(ii) Let the width in the map be q

Therefore, Width in MapActual Width = 15000

q1km = 15000

⟹ q = 1km5000

⟹ q = 1×1055000 cm

⟹ q = 20 cm


2. The length of a building is 40 m and the length of its model is 50 cm. Find the area of the terrace of the building if the area of the terrace in the model is 1400 cm2.

Solution:

Let the scale factor = k

Therefore, k = Length of the BuildingLength of the Model

          = 40m50cm

          = 40×100cm50cm

          = 80 cm

Let the area of the terrace of the building = a

Area of the Terrace of the BuildingArea of the Terrace in the Model = k2

Therefore, a1400cm2 = 80 × 80

⟹ a = 80 × 80 × 1400 cm2

⟹ a = 80×80×1400100×100 m2

⟹ a = 896 m2





9th Grade Math

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