Math, asked by mechandan283, 6 months ago

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

Answered by Anonymous
26

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

Answered by anindyaadhikari13
8

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)

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