HOW TO FIND MISSING DIAGONAL OF A KITE

Find the length of the missing diagonal in each kite.

Problem 1 :

Find HF if GE = 43 yd.

Solution :

GE = 43 yd, Area = 258 yd²

To find HF :

Area = 1/2 (d1 × d2)

d₁ = 43, d₂ = ?

258 = 1/2 (43 × d2)

258 = 21.5 × d2

258/21.5 = d2

12 = d2

So, HF = 12 yd.

Problem 2 :

Find NL if MK = 18 in.

Solution :

MK = 18 in, Area = 324 in²

To find NL :

Area = 1/2 (d1 × d2)

d1 = 18, d2 = ?

324 = 1/2 (18 × d2)

324 = 9 × d2

324/9 = d2

36 = d2

So, NL = 36 in.

Problem 3 :

Find BD if AC = 47 yd.

Solution :

AC = 47 yd, Area = 493.5 yd²

To find BD :

Area = 1/2 (d1 × d2)

d1 = 47, d2 = ?

493.5 = 1/2 (47 × d2)

493.5 = 23.5 × d2

493.5/23.5 = d2

21 = d2

So, BD = 21 yd.

Problem 4 :

Find TV if SU = 30 ft.

Solution :

SU = 30 ft, Area = 153 ft²

To find SU :

Area = 1/2 (d1 × d2)

d1 = 30, d2 = ?

153 = 1/2 (30 × d2)

153 = 15 × d2

153/15 = d2

10.2 = d2

So, TV = 10.2 ft.

Problem 5 :

Find EG if DF = 15 ft.

Solution :

DF = 15 ft, Area = 360 ft²

To find EG :

Area = 1/2 (d1 × d2)

d1 = 15, d2 = ?

360 = 1/2 (15 × d2)

360 = 7.5 × d2

360/7.5 = d2

48 = d2

So, EG = 48 ft.

Problem 6 :

Find XZ if WY = 32 in.

Solution :

WY = 32 in, Area = 432 in²

To find XZ :

Area = 1/2 (d1 × d2)

d1 = 32, d2 = ?

432 = 1/2 (32 × d2)

432 = 16 × d2

432/16 = d2

27 = d2

So, XZ = 27 in.

Problem 7 :

Find QS if PR = 11 yd.

Solution :

PR = 11 yd, Area = 253 yd²

To find QS :

Area = 1/2 (d1 × d2)

d1 = 11, d2 = ?

253 = 1/2 (11 × d2)

253 = 5.5 × d2

253/5.5 = d2

46 = d2

So, QS = 46 yd.

Problem 8 :

The area of rhombus 90 square units. If one diagonal is 10 units, find the length of the other diagonal.

Solution :

Area of rhombus = 90 square units

1/2 (d₁ × d₂) = 90

Length of one diagonal (d₁) = 10 units

(1/2) x 10 x d₂ = 90

5d₂ = 90

d₂ = 90 / 5

= 18

Problem 9 :

The rhombus has perimeter of 100 meters and a diagonal 30 meters long. Find the area of the rhombus.

Solution :

Perimeter of rhombus = 100 meters

4a = 100

a = 100/4

a = 25

Length of one diagonal = 30 meters

half of the length of diagonal = 15 meters

Let x be the half length of other diagonal.

30² = 15² + x²

900 = 225 + x²

x² = 900 - 225

x² = 675

x = √675

x = √(5 x 5 x 3 x 3 x 3)

= 5 x 3√3

= 15√3

2x = 2(15√3)

= 30√3

Area of rhombus = 1/2 (d₁ × d₂)

= (1/2) x 30 x 30√3

= 15 x 30√3

= 450√3

Problem 10 :

The rhombus has an area of 20 and one diagonal of length 12. Find the length of the other diagonal.

Solution :

Area of rhombus = 20 square units

Length of one diagonal = 12 units

Length of other diagonal = d

1/2 (d₁ × d) = 20

1/2 (12 × d) = 20

6d = 20

d = 20/6

d = 3.3 units 

So, the length of other diagonal is 3.3 units.

Problem 11 :

The length of one of its diagonals of a kite is 4 cm longer than twice the length of the other diagonal. The area of the kite is 15 cm². Find the length of the other diagonal.

Solution :

Let the diagonals of kite be d1 and d2.

d₁ = 2d₂ + 4

Area of kite = 15 cm²

1/2 (d₁ × d₂) = 15

1/2 (2d₂ + 4) × d₂ = 15

2d₂² + 4d₂ = 15(2)

d₂² + 2d₂ = 15

Let t = d₂

t² + 2t = 15

t² + 2t - 15 = 0

(t + 5)(t  - 3) = 0

t = -5 and t = 3

d₂ = 3 

The length of the other diagonal is 3 units.

d₁ = 2(3) + 4

= 6 + 4

d₁ = 10 units

So, the length of diagonals are 10 units and 3 units.