Question

the area of a parallelogram with base 25cm and altitude 16cm is equal to the area of a rhombus whose diagonal is 40 cm. find the length of the other diognal?​

Answer 1

area of llgm = 25×16

=400

area of llgm = area of rhombus

area of rhombus=1/2×diagnal×length

400=1/2×40×length

length=20cm

Answer 2

The length of the other diagonal is 20 cm.

Explanation:

Area of parallelogram = Base x Corresponding altitude     (i)

Area of Rhombus = 0.5 x Diagonal 1 x Diagonal 2                 (ii)

Given : Base of parallelogram = 25cm

Altitude = 16 cm

Area of parallelogram= 25 x 16 =400 sq. cm  (By (ii))

Area of rhombus = Area of parallelogram = 400 sq. cm

Length of Diagonal 1 of rhombus = 40 cm , Then

400 = (0.5) x (40 ) x  (Diagonal 2)  ( by (i))

⇒ 400 = (20 ) x  (Diagonal 2)

⇒ Diagonal 2 = $\dfrac{400}{20}=20\ cm$

Hence, the length of the other diagonal is 20 cm.

# Learn more :

i) Find the area of a rhombus whose diagonals are of lengths 20 cm and 16cm

https://brainly.in/question/2737026

ii) The area of a parallelogram with Base 25cm and altitude 15cm is equal to the area of a rhombus whose one diagonal is 30cm. find the length of the other diagonal of the rhombus.

https://brainly.in/question/1186419