Question

2. The area of a rhombus is 48 cm' and its perim-
eter is 20 cm. What is its height ?​

Answer 1

perimeter=4a

20=4a

a=5cm

area = base × height

48=5×h

h=48/5

h=9.6cm

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Explanation:

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Answer 2

Answer:

the the answer is 48 square cm.

explanation:

the area of rhombus is 48 cm square and its perimeter is 20cm.

the side of a rhombus is20/4 =5cm. the the hypotenuse of the RAT is 5cm.

area of each RAT= 48/12 sq cm , hence the height of each RAT the hypotenuse at the base is 12/5 =2.4cm.

considered considered one of the RAT, say ABC, right angle at B. from B drop BD as a perpendicular on AC which is hypotenuse and 5 cm long.

let AD= x, DC=(5-x), ABD nd BCD are similar triangle. thus, AD/BD

=BD/CD or

x/BD=BD/(5-x)

x^2-5+5.76=0 or

x=[5+(5^2-4*5.76)^0.5]/2

=[5+1.4]/2=6.4/2 =3.2 cm=AD

In RAT, ABD. AB^2= AD^2 + BD^2=3.2^2+2.4^2=10.24+5.76 = 16 or AB=4cm

area of ABC is equals to 48/4=12 cm sq. so if AB = to 4 cm, BC should be 12×2/4=6cm.

the diagonals of the Rhombus are therefore 8 cm and 12 cm which give area of Rhombus as 8*12/2 = 48sq cm.