Problem 1 :
A 20 cm wide picture frame surrounds a painting which is 100 cm by 60 cm. Are the two rectangles shown here similar?
Solution :
Picture frame = 20 cm
Surrounds a painting = 100 cm by 60 cm
100 : 60 = 5 : 3
Inside rectangle has sides in 5 : 3
100 + 60 = 160
20 cm wide picture frame = 160 – 20
= 140
140 : 100 = 7 : 5
Outside rectangle has sides in 7 : 5
And 5 : 3 ≠ 7 : 5
Therefore it is not similar.
Give brief reasons why these figures possess similar triangles:
Problem 2 :
Solution :
∠ABE = ∠DEB (Alternate interior angles)
∠ACB = ∠DCE (Vertically opposite angles)
So, triangles are equiangular and therefore, similar.
Problem 3 :
Solution :
∠PQR = ∠STR (given)
∠PQT = ∠STP (Alternate interior angles)
∠PRQ = ∠SRT (Vertically opposite angles)
So, triangles are equiangular and therefore, similar.
Problem 4 :
Solution :
Both triangles are right angled.
∠BAE = ∠EDA (Alternate interior angles)
∠BCA = ∠DCE (Vertically opposite angles)
So, triangles are equiangular and therefore similar.
Problem 5 :
At 4 pm one day the shadow of a pine tree was 5 m long. At the same time a 2 m long broom handle had a shadow which was 3 m long. How high is the pine tree?
Solution :
The shadow of a pine tree = 5 m long
The same time = 2 m long
Broom handle had a shadow = 3 m long
2/3 = x/5
10 = 3x
x = 3.3
So, the pine tree high is 3.3 m.
After establishing similarity, find the unknowns in:
Problem 6 :
Solution :
6/4 = x/2
3/2 = x/2
x = 3
Problem 7 :
Solution :
12/10 = x/4
6/5 = x/4
x = 4.8
Problem 8 :
Solution :
x/4 = 7/3
3x = 28
x = 9 1/3
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM