CASE STUDY QUESTION 30-Class X-Maths

CASE STUDY QUESTION 30-Class X-Maths

A scale drawing of an object is the same shape at the object but a different size. The scale of a drawing Is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. The ratio of two corresponding sides in similar figures is called the scale factor.

If one shape can become another using revising, then the shapes are similar. Hence, two shapes are similar when one can become the other after a resize, flip, slide or turn. In the photograph below showing the side of a train engine. Scale is 1 : 200.

This means that a length of 1 cm on the photograph above corresponds to a length of 200 cm, or 2 metres, on the actual engine. The scale can also be written as the ratio of two lengths.

(a) The overall length of the engine in the photograph above, including the couplings if the length of the model is 11 cm is :
(i) 22 cm (ii) 220 cm (iii) 220 m (iv) 22 m

Ans: Length of the engine = 11 x 200 = 2200 cm
= 22 m

(b) What will affect the similarity of any two polygons?
(i) They are flipped horizontally
(ii) They are dilated by a scale factor
(iii) They are translated down
(iv) They are not the mirror image of one another

Ans: (iv) They are not the mirror image of one another

(c) What is the actual width of the door if the width of the door in photograph is 0.35 cm?
(i) 0.7 m (ii) 0.7 cm (iii) 0.07 cm (iv) 0.07 m

Ans: Actual width of the door = 0.35 x 200 = 70 cm = 0.7 m

(d) If two similar triangles have a scale factor of 5 : 3, which statement regarding the two triangles is true?
(i) The ratio of their perimeters is 15 : 1
(ii) Their altitudes have a ratio 25 : 15
(iii) Their medians have a ratio 10 : 4
(iv) Their angle bisectors have a ratio 11 : 5

Ans: (ii) Their altitudes have a ratio 25 : 15

(e) The length of AB in the given figure is :
(i) 8 cm (ii) 6 cm (iii) 4 cm (iv) 10 cm