In the given figure, given that ∆ABC ∼ ∆PQR and quad ABCD ∼ quad PQRS. Determine the value of x, y, z in each case.
Answers
SOLUTION :
(i) Given :
∆ABC ∼ ∆PQR , AB = 12 , BC= 7 , AC = 10 , PQ = 9 , QR = x , PR = 9
AB/PQ = BC/QR = AC/PR
[since triangles are similar, hence corresponding sides will be proportional]
12/9 = 7/x = 10/y
12/9 = 7/x
12x = 9 ×7
x = (9×7)/12 = (3 × 7) /4
x = 21/4
12/9 = 10/y
12y = 10 × 9
y = (10 × 9)/12 =( 5 × 9 )/6 = 5 × 3 /2
y = 15/2
Hence, the values of x = 21/4 & y = 15/2.
(ii)
Given :
∆ABCD ∼ ∆PQRS , AB = 16 , BC= 50 , DC = 50/3 , AD = 20, PQ = x , QR = y , RS = z, PS = 7
AB/PQ = BC/QR = CD/RS =DA/SP
[since quadrilaterals are similar, hence corresponding sides will be proportional]
20/7 = 16/x = 50/y = 50/3z
20/7 = 16/x
20x = 16× 7
x = (16×7)/20
x = 4×7 / 5
x = 28/5
20/7 = 50/y
20y = 50 × 7
y =(50×7)/20
y = 35 /2
20/7 = 50/3z
20 × 3z = 50 × 7
60z = 350
z = 350/60
z = 35/6
Hence, the values of x = 28/5 , y = 35/2 & z = 35/6.
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