HOW TO FIND LENGTH OF A SIDES OF A KITE

Definition of kite :

A kite is a quadrilateral which has two pairs of adjacent sides equal in length.

In the kite given above,

AB = AC and BC = DC

Find the values of the variables. Then find the lengths of the sides.

Problem 1 :

Solution :

AB = 4.5, AD = b - 2.3

AB = AD

4.5 = b – 2.3

Add 2.3 to both sides.

4.5 + 2.3 = b – 2.3 + 2.3

6.8 = b

b = 6.8

BC = DC

a – 1.4 = 2a – 7

Comparing like terms.

a – 2a = -7 + 1.4

-a = -5.6

a = 5.6

BC = a - 1.4

Applying the value of a, we get

BC = 5.6 - 1.4

BC = 4.2

So, the lengths of the sides are

AB = 4.5, AD = 4.5, BC = 4.2 and DC = 4.2

Problem 2 :

Solution :

By observing the figure,

3m = n

3m - n = 0 ----(1)

7m - 14 = n + 6

7m - n = 6 + 14

7m - n = 20 -----(2)

(1) - (2)

3m - n - (7m - n) = 0 - 20

3m - n - 7m + n = -20

-4m = -20

m = 5

By applying the value of m in (1), we get

3(15) = n

n = 45

AB = 3m ==> 3(5) ==> 15

AB and AD is 15.

DC = n + 6

DC = 45 + 6 ==> 51

BC and DC are 51.

Problem 3 :

Determine the value of x for which EFGH is a kite.

Solution :

EF = FG

4x – 5 = 20 – x

Comparing like terms.

4x + x = 20 + 5

5x = 25

Divide both sides by 5.

5x/5 = 25/5

x = 5

So, the value of x is 5.

Problem 4 :

Find the value of x in the following kite.

Solution :

Since it kite,

AB = AD and BC = DC

6x - 3 = 21

6x = 21 + 3

6x = 24

x = 24/6

x = 4

Problem 5 :

Find the perimeter of the kite.

Solution :

XY = 35 cm, XW = 35 cm, YZ = 60 cm and WZ = 60 cm

Perimeter of kite = XY + XW + YZ + WZ

= 35 + 35 + 60 + 60

= 70 + 120

= 190 cm

So, the perimeter of the kite is 190 cm.

Problem 6 :

Scientists are researching solar sails, which move spacecraft using radiation pressure from sunlight. What is the area of the solar sail shown? Explain your reasoning.

Solution :

Length of diagonal 1 = 4 + 4

= 8 m

Length of diagonal 2 = 4.5 + 3.5

= 8 m

Area of kite = (1/2) x diagonal 1 x diagonal 2

= (1/2) x 8 x 8

= 64/2

= 32 square meter.

Problem 7 :

You use 94 inches of plastic to frame the perimeter of a kite. One side of the kite has a length of 18 inches. Find the length of each of the three remaining sides

Solution :

Perimeter of kite = 94 inches

One side length of kite = 18 inches

Then, the other side length of kite = 18 inches

Let x be the other two equal sides.

x + x + 18 + 18 = 94

2x + 36 = 94

2x = 94 - 36

2x = 58

x = 58/2

x = 29

So, the length of the remaining three sides are 18 m, 29 m and 29 m.

Problem 8 :

Given kite ABCD, find AB

CB = 3x + 6, BD = 8x - 9 and AB = 7x - 1

Solution :

CB = BD

3x + 6 = 8x - 9

3x - 8x = -9 - 6

-5x = -15

x = 15/5

x = 3

Applying the value of x in AB = 7x - 1

= 7(3) - 1

= 21 - 1

= 20

Problem 9 :

Given kite ABCD, find X and Y

Solution :

x = 40

The diagonals will intersect at 90 degree.

40 + Y + 90 = 180

130 + Y = 180

Y = 180 - 130

Y = 50

So, the values of X and Y are 40 and 50 respectively.

Problem 10 :

Find x given that kite ABCD.

Solution :

∠ADB = 35

∠ADB = ∠ABD

4x - 13 = 35

4x = 35 + 13

4x = 48

x = 48/4

x = 12

So, the value of x is 12.

Problem 11 :

Kite's perimeter = 86 ft, find x and y

Solution :

5x - 15 = 2x + 3

5x - 2x = 3 + 15

3x = 18

x = 18/3

x = 6

Perimeter of kite = 86 ft

3y + 3y + 6y - 2 + 6y - 2 = 86

6y + 12y - 4 = 86

18y = 86 + 4

18y = 90

y = 90/18

y = 5

So, the values of x and y are 6 and 5 respectively.