Draw a line segment of length 7.6cm and divide it in the ratio 5:8. Measure the two parts
Answers
Answer: The above question can be solved by either basic proportionality theorem by using a diagram or by the linear equation in two variables without using any diagram.
Step-by-step explanation:
Linear equation in two variables method,
Consider, a line segment of 7.6 cm which can be divided into two variables i.e. variable 'X' and variable 'Y'.
Step-1:-
x+ y = 7.6 cm
Now, the ratio in which the line segment is to be divided i.e ratio of 5:8
Step-2:-
x:y= 5:8
Multiplying both sides, we get-
8x= 5y OR 8x-5y=0 - linear equation no.1
x+y= 7.6 - linear equation no.2
Step-3:- From equation-2, we get
y= 7.6-x
Putting this value of y in equation-1,
we get,
8x-5(7.6-x)=0
8x-38+ 5x=0
13x=38
x= 2.9
Step-4:- Putting the value of x in equation-2
we get, y= 4.5
Answer- The measurements to which the line segment is divided in the ratio 5:8 are- 2.9 cm and 4.5 cm.
Step-by-step explanation:
Given :-
A line segment of length 7.6 cm
To find :-
Dividing it in the ratio 5:8 and the lengths of two parts
Solution :-
(See above attachment for construction )
Given that
The length of the given line segment = 7.6 cm
Given ratio = 5:8
Total parts are 5+8 = 13 parts
Therefore, 13 parts = 7.6 cm
=> 1 part = 7.6 / 13 cm
=> 1 part = 0.584 cm (approximately)
Now,
5 parts = 5×0.584 = 2.92 cm = 2.9 cm
8 parts = 8×0.584 = 4.672 cm = 4.7 cm
Construction :-
→ Draw a linesegment AB of length 7.6 cm
→ Construct an acute angle ∠BAX at A
→ Mark off 5+8 = 13 equal parts( A₁ = A₂ =...= A₁₃)on AX with same radius .
→ Join A₁₃ and B
→ Draw a line parallel to A₁₃ B at A5 meeting AB at C.
→ Now, the point C divides AB in the ratio 5:3
→ Measure AC and BC
We have, AC = 2.9 cm and BC = 4.7 cm
AB = AC+BC = 2.9 + 4.7 = 7.6 cm
