Question

find the length of the other diagnol of a rhombus whose perimeter is 60 cm and one diagnol measure is 18 cm. asap pls . i have an exam tomorrow. ​

Answer 1

Step-by-step explanation:

area=1/2×d1×d2

60 =1/2×18×d2

60=9×d2

60÷9=d2

6.66=d2

Answer 2

Answer: 24 cm

Step-by-step explanation:

Let the side of the rhombus be s.

Perimeter of Rhombus = 4s

⇒ 60 = 4s

⇒ s = 60 ÷ 4 = 15 cm

Let the rhombus be ABCD as shown in the attachment.

Let's take AD = 60cm.

We Know That, the diagonals of a rhombus bisect each other.

⇒ OD = 1/2 of AD = 1/2 × 18 = 9 cm

We Know That, the diagonals of a rhombus bisect each other at right angles.

∴ ΔCOD is a right angled triangle.

In ΔCOD by Pythagoras' Theorem,

(OD)² + (OC)² = (CD)²

⇒ 9² + (OC)² = 15²

⇒ 81 + (OC)² = 225

⇒ (OC)² = 225 - 81

⇒ (OC)² = 144

⇒ OC = √144 = 12 cm

∴ BC = 2 × OC = 2 × 12 = 24 cm

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