Question

the perimeter of a rhombus is 328cm. one of the digonal is 160cm. find the length of the other diagonal area of the rhombus

Answer 1

Step-by-step explanation:

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Answer 2

$\sf{Answer}$

Given :-

• Perimeter of Rhombus is 328 cm
• One of diagonal is 160 cm

To find :-

• Other diagonal of rhombus
• Area of rhombus

Formula to know :-

Area of rhombus = 1/2 d1 × d2

Perimeter of rhombus = 4a

Lets do!

Given that perimeter of rhombus is 328 cm

But we know perimeter of rhombus is 4a

So,

4a = 328 cm

a = 328 /4 cm

a = 82 cm

Side of rhombus is 82cm

One diagonal is 160cm

Let

BD ,AC are diagonals of rhombus

BD = 160cm

BO = OD = 80cm (160/2)

And

AB = 82cm

BO = 80cm

From pythagoras theoram

AO² + OB² = AB²

AO² + (80)² = (82)²

AO² + 6400 = 6724

AO² = 6724 - 6400

AO² = 324

AO² = 18²

AO = 18

If AO = 18 OC also 18 cm

Then AC = 18+18

AC = 36 cm

So, other diagonal is 36cm

Area of rhombus = $\sf\dfrac{1}{2}$ d1 d2

d1 = 160cm

d2 = 36cm

Area of rhombus = $\sf\dfrac{1}{2}$ (160)(36)

Area of rhombus =( 160 ) ( 18)

Area of rhombus = 2880cm²