Question

The perimeter of a rhombus is 100 cm and one diagonal is 48 cm. Find (a) the length of the other diagonal (b) the area of the rhombus.

Pls explain with step by step explaination​

Answer 1

Answer:

600cm2

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Step-by-step explanation:

The perimeter of the rhombus is 100 cm.

It is known that all sides of rhombus are equal.

Let the length of side of rhombus be x,

Then perimeter of rhombus is 4x

Thus, 4x=100x=25

Hence, the length of each side of the rhombus is 25 cm.

We are given that the length of one of its diagonal is 30

In a rhombus, diagonals are perpendicular bisectors

Let diagonals bisect at O.

Let AC be 30 cm., then the length of AO

is 302=15cm

Also, triangle ΔAOB is a right triangle.

Apply Pythagoras theorem in ΔAOB

AB2=AO2+OB2

We have AB=25cm and AO=15cm,

Therefore,

(25)2=(15)2+OB2OB2=(25)2−(15)2

Simplifying the expression using the formula a2−b2=(a+b)(a−b)

OB2=(25)2−(15)2OB2=(25+15)(25−15)OB2=40(10)OB2=400OB=20

Hence, the length of the other diagonal will be twice the length OB, which is 40units.

Next, we will find the area of the rhombus whose formula is d1×d22, where d1 and d2 are the length of diagonals.

Thus, area of rhombus is,

40×302=12002=600cm2