Advertisements
Advertisements
Question
Find the scale factor in each of the following and state the type of size transformation:
Model area = 75cm2, Actual area = 3cm2
Solution
Model area = 75cm2, Actual area = 3cm2
Actual area
= 3 x 10000cm2
= 30000cm2
Scale factor
= `sqrt(("Model Area")/("Actual Area")`
= `sqrt((75)/(30000)`
= `sqrt((1)/(400)`
= `(1)/(20)`
Scale factor = 0.05
Since the scale factor < 1 and > 0
⇒ Type of size transformation = reduction.
APPEARS IN
RELATED QUESTIONS
In the given figure, AB and DE are perpendicular to BC.
1) Prove that ΔABC ∼ ΔDEC
2) If AB = 6 cm; DE = 4 cm and AC = 15 cm. Calculate CD.
3) Find the ratio of area of ΔABC: area of ΔDEC
In the figure, given below, the medians BD and CE of a triangle ABC meet at G. Prove that:
- ΔEGD ~ ΔCGB and
- BG = 2GD from (i) above.
The given diagram shows two isosceles triangles which are similar. In the given diagram, PQ and BC are not parallel; PC = 4, AQ = 3, QB = 12, BC = 15 and AP = PQ.
Calculate:
- the length of AP,
- the ratio of the areas of triangle APQ and triangle ABC.
In Figure 3, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. If arcs of equal radii 7 cm have been drawn, with centres A,B, C and D, then find the area of the shaded region.
On a map drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and ∠ABC = 90°.
Calculate : the actual lengths of AB and BC in km.
Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are `3/5` of the corresponding sides of the first triangle.
In the given figure, ABC is a triangle. DE is parallel to BC and `"AD"/"DB" = (3)/(2)`.
(i) Determine the ratios `"AD"/"AB","DE"/"BC"`.
(ii) Prove that ΔDEF is similar to ΔCBF.
Hence, find `"EF"/"FB"`.
(iii) What is the ratio of the areas of ΔDEF and ΔBFC?
In ΔABC, point D divides AB in the ratio 5:7, Find: BC, If DE = 2.5cm
On a map drawn to a scale of 1:25000, a triangular plot of land is right angled and the sides forming the right angle measure 225cm and 64cm.Find: The actual length of the sides in km
ABCD is a parallelogram. Point P divides AB in the ratio 2:3 and point Q divides DC in the ratio 4:1. Prove that OC is half of OA.
