Question

A parallelogram with the perimeter of 44 cm is divided by the diagonal into four triangles. The
difference between the perimeters of two adjacent triangles is 6cm. Find the dimensions of the
parallelogram​

Answer 1

Answer:

Sides of parallelogram  =  8  & 14 cm

Step-by-step explanation:

Step-by-step explanation:

Let say sides of parallelogram are a & b

then 2(a + b) = 44

=> a + b = 22

Let say diagonal length are 2d₁  & 2d₂

Then Half of Diagonal = d₁ & d₂

Perimeter of one triangle

= a + d₁ + d₂

Perimeter of another triangle

= b + d₁ + d₂

a + d₁ + d₂ = b + d₁ + d₂  + 6

=> a = b + 6

  a + b = 22

=> b + 6 + b = 22

=> 2b = 16

=> b = 8

a =b + 6 = 14

Sides of parallelogram  =  8  & 14 cm

Answer 2

Answer:

The dimensions of the parallelogram are 18 cm × 4 cm.

Step-by-step explanation:

From the above question,

They have given :

A parallelogram with the perimeter of 44 cm is divided by the diagonal into four triangles. The difference between the perimeters of two adjacent triangles is 6cm.

Here we need to find the dimensions of the parallelogram​.

Let the length of the parallelogram be x cm and the breadth be y cm.

The perimeter of the parallelogram can be written as

P = 2(x + y)

Substituting 44 cm for P,

44 = 2(x + y)

x + y = 22

The perimeter of the two adjacent triangles is

P' = x + y - 6

Substituting 22 - 6 for P',

x + y - 6 = 16

Adding 6 to both sides,

x + y = 22

The two equations x + y = 22 and x + y - 6 = 16 can be solved simultaneously to get

x = 18 cm and y = 4 cm

The dimensions of the parallelogram are 18 cm × 4 cm.

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