Question

The area of rhombus is 480cm square and one of its diagonals measures 48cm.find a.length of other diagonal.b) length of each of its sides.c)its perimeter

Answer 1

"The area of the rhombus = 480 sq cm

Diagonal d1 = 48 cm.

Diagonal d2 = ? cm.

Area of rhombus = d1*d2/2 = 36*d2/2 = 480, or

i) d2 = 480*2/48 = 20 cm.

Side of rhombus =[(d1/2)^2+(d2/2)^2]^0.5 = [48^2+20^2]^0.5

= [576+100]^0.5

= 676^0.5

= 26 cm.

ii) Diagonal d2 = 48 cm, sides = 26 cm.

iii) Perimeter=4*26=104 cm

"

Answer 2

Find the length of the other diagonal:

Area of a rhombus = 1/2(Diagonal 1 x Diagonal 2)

480 = 1/2 (48 x Diagonal 2)

48 x Diagonal 2 = 960

Diagonal 2 = 20 cm

Find the length of its side:

half of each diagonal and the side make a right angle triangle

a² + b² = c²

(20÷2)² + (48÷2)² = c²

c² = 676

c = 26 cm

Find the perimeter:

Perimeter = 4 x Length

Perimeter = 4 x 26 = 104 cm

Answer: (a) Diagonal = 20 cm (b) length = 26 cm (c) Perimeter = 104 cm