the length of the sides of a duadilateral are in the ratio 1:2:3:4 of the sum all sides is 50 cm find all the four sides
Answers
Question :-
The length of the sides of a quadilateral are in the ratio 1:2:3:4 and the sum all sides is 50 cm. Find all the four sides.
Solution :-
Length of all sides = 50 cm
Let the ratio of the sides be 1x , 2x , 3x , 4x
➾ 1x + 2x + 3x + 4x = 50
➾ 10x = 50
➾ x = 50/10
➾ x = 5
Substituting the values,
➛Length of 1st side = 1x = 1×5 = 5 cm
➛Length of 2nd side = 2x =2×5 =10 cm
➛Length of 3rd side = 3x =3×5 = 15 cm
➛Length of 4th side = 4x =4×5 = 20cm
Correct Question:-
➡ The length of the sides of a quadrilateral are in the ratio 1 : 2 : 3 : 4 and the sum of all sides is 50 cm. Find all the four sides.
Answer:-
➡ The measures of 4 sides are 5cm, 10cm, 15cm and 20cm respectively.
Solution:-
➡ This can be done in two ways.
Process 1:-
Given that,
➡ Length of the sides are in the ratio 1 : 2 : 3 : 4
Therefore,
➡ Sum of the ratio = 1 + 2 + 3 + 4 = 10
Now,
➡ Sum of all sides of the quadrilateral = 50cm.
Therefore,
➡ Length of first side = 1/10×50 cm = 1×5cm = 5cm.
➡ Length of second side = 2/10×50 cm = 2×5cm = 10cm.
➡ Length of third side = 3/10×50 cm = 3×5cm = 15cm.
➡ Length of the fourth side = 4/10×50 cm = 4×5cm = 20cm.
Hence, the length of the sides of the given quadrilateral are 5cm, 10cm, 15cm and 20cm.
Process 2:-
➡ Let the sides of the rectangle be x cm, 2x cm, 3x cm, 4x cm.
Therefore, according to the given condition,
➡ x + 2x + 3x + 4x = 50
➡ 10x = 50
Dividing both sides by 10, we get,
➡ x = 10
Putting the value of x, we get,
➡ Length of first side = 1×5cm = 5 cm.
➡ Length of the second side = 2×5 cm = 10cm.
➡ Length of the third side = 3×5 cm = 15cm.
➡ Length of the fourth side = 4×5 cm = 20cm.
Hence, the length of the sides of the given quadrilateral are 5cm, 10cm, 15cm and 20cm.
Verification:-
Let us verify our result.
Length of 4sides are 5cm, 10cm, 15cm and 20cm.
Ratio
= 5 : 10 : 15 : 20
= 1 : 2 : 3 : 4.
Hence, ratio remains same.
Hence, answer is correct. (Verified)