Two hotels are at the ground level an either side of a mountain. On moving certain dance the top of the mountain two huts are situated as shown in the figure. The ratio between the distance from hotel B to hut-2 to that of hut-2 to mountaintop is 3:7.
Question41 What is the ratio of the perimeters of the triangle formed by both hotels and miltintais top to the triangle formed by both huts and mountain top?
a.5:2
b.7:3
c.3:10
d.10:3
Question42 The distance between the hotel A and hit-1 is? a.2.5 miles
a.2.5 miles
b.4.29 miles
c.29 miles
d.1.5 miles
Question43 If the horizontal distance between the hut-1 and hut-2 is 8 miles, then the distance between 2 hotel is?
a.9 miles
b.2.4 miles
c.11.43 miles
d.7 miles
Question44 If the distance from mountain top to hut-1 is 5 miles more than that of distance between hut-2 and mountain top?
a.5.5 miles
b.6 miles
c.3.5 miles
d.4 miles
Question45 What is the ratio of areas of two parts formed in the complete figure?
a. 53:21
b.49:51
c.10:41
d.51:33
Answers
Given : Two hotels are at the ground level an either side of a mountain. On moving certain dance the top of the mountain two huts are situated as shown in the figure. The ratio between the distance from hotel B to hut-2 to that of hut-2 to mountaintop is 3:7.
To Find: the ratio of the perimeters of the triangle formed by both hotels and mountain top to the triangle formed by both huts and mountain top
The distance between the hotel A and hut-1
Solution:
From the figure line between Huts parallel to line between Hotels A and B
=> Triangles formed by Hotels and Huts with Mountain top are Similar
The ratio between the distance from hotel B to hut-2 to that of hut-2 to mountaintop is 3:7.
=> The ratio between the distance from hotel B to mountaintop and hotel B to mountaintop is (3 + 7) : 7 = 10:7
ratio of the perimeters of the triangle formed by both hotels and mountain top to the triangle formed by both huts and mountain top is same as side ratio = 10:7
The distance between the hotel A and hut-1 = x
=> x/10 = 3/7
=> x = 30/7 = 4.286 = 4.29 miles
Learn More:
थेल्स प्रमेय(BPT) का कथन लिखकर उसे ...
brainly.in/question/21435493
In Figure 2, DE || BC. Find the length of side AD, given that AE = 1.8 ...
brainly.in/question/25629198
Answer:
see
Step-by-step explanation:
i) (b): Let ΔABC is the triangle formed by both hotels and mountain top. ΔCDE is the triangle formed by both huts and mountain top. Clearly, DE || AB and so
△ABC∼△DEC [By AA-similarity criterion]
Now, required ratio = Ratio of their corresponding sides =BCEC=107 i.e., 10:7.
(ii) (c): Since, DE || AB, therefore
CDAD=CEEB⇒10AD=73⇒AD=10×37=4.29 miles
(iii) (b) : Since, △ABC∼△DEC
∴BCEC=ABDE [ ∵ Corresponding sides of similar triangles are proportional]
⇒107=AB8⇒AB=807=11.43 miles
(iv) (a) Given, DC= 5+ BC.
Clearly, BC = 10-5 = 5 miles
Now, CE = 710x BC = 710 x 5 = 3.5 miles
(v) (d) :Clearly the radio of areas of two angles (i,e △ABC∼△DEC)
=(BCEC)2=(107)2=10049∴ Required ratio =ar(ΔCDE)ar(EBAD)=49100−49=4951