Question

One side of a kite is 5 cm less than 2 times the length of another. If the perimeter is 14 cm, find the length of each side of the kite.

A) 5 cm, 5 cm

B) 4.2 cm, 3.4 cm

C) 6.3 cm, 7.7 cm

D) 4 cm, 3 cm

Answer 1

D) 4 cm, 3 cm

Step-by-step explanation:

Since we know that kite is made of two sets of equal sides.

Let x be the length of one of equal sides and y be length of another side of equal sides.

We have been given that one side of a kite is 5 cm less than 2 times the length of another. We can represent this information as:

`x+5=2y...(1)`

We are also told that the perimeter is 14 cm. We can represent this information as:

`2(x+y)=14...(2)`

From equation (1) we will get,

`x=2y-5`

Substituting this value in equation (2) we will get,

`2(2y-5+y)=14`

`2(3y-5)=14`

`6y-10=14`

`6y-10+10=14+10`

`6y=24`

`y=(24)/(6)`

`y=4`

Therefore, length of one side of kite is 4 cm.

Upon substituting y=4 in equation (1) we will get,

`x+5=2*4`

`x+5=8`

`x+5-5=8-5`

`x=3`

Therefore, the length of another side of kite is 3 cm and option D is the correct choice.

Answer 2

Explanation:

Alright, lets get started.

Suppose one side of the kite is x

One side of a kite is 5 cm less than 2 times the length of another.

So, another side of the kite will be =
`2x-5`

So, the all 4 sides of the kite will be x, x , 2x-5 and 2x-5

The perimeter of the kite will be =
`x+x+2x-5+2x-5=6x-10`

As per given in question, perimeter is 14, so

`6x-10=14`

Adding 10 in both sides

`6x=24`

Dividing 6 in both sides

`x=4`

So, another side is
`2*4-5=3`

So, the sides are 4 cms and 3 cms : Answer D

Hope it will help :)