Question

This square is formed using three identical rectangles. If the perimeter of the square is 120 cm, find the perimeter of each rectangle.

Answer 1

Given:

• three identical rectangles form the square
• the perimeter of the square = 120 cm

To find:

• the perimeter of each rectangle

Solution:

We know that the perimeter of a square is side × 4.

Here, s × 4 = 120 cm.

⇒ s = 120/4

⇒ s = 30

So, each side of the square measures 30 cm.

Now, let's take rectangle ABCD (as in the attachment) to find the perimeter of each rectangle since they are identical.

Because of their identicalness, three times the measure of AB (the breadth of the rectangles) is the measure of the side of the square. So,

⇒ AB × 3 = 30 cm

⇒ AB = 30/3

⇒ AB = 10 cm

Now we have the following measures of the rectangle ABCD:

• AB = CD = 10 cm
• DA = BC = 30 cm (the length of the rectangle is the side of the square)

To calculate the perimeter of the rectangle, these measurements are exactly what we need.

Perimeter of a rectangle = 2 × (l + b)

Perimeter of rectangle ABCD:

⇒ 2 × (10 + 30)

⇒ 2 × 40

⇒ 80 cm

Therefore, the perimeter of each rectangle is 80 cm.

Answer 2

Answer:

The perimeter of each rectangle is $80cm$

Step-by-step explanation:

We know that the perimeter of a square is $4\times side$

Now given that perimeter of square is $120cm$

So,

$side\times 4=120 cm\\side=\frac{120}{4} \\side=30$

Therefore, each side of the square measures is $30cm$

Now it is given that the perimeter of each rectangle are identical.

Because of their identicalness, three times the measure of the breadth of the rectangles is the measure of the side of the square.

$Breadth\times3=30cm\\Breadth=\frac{30}{3}\\Breadth=10cm$

Now the perimeter of rectangle is:

We know that perimeter of rectangle is$=2\times(l+b)$

Now substitute the known values, we get

$Perimeter=2\times(10+30)\\Perimeter=2\times40\\Perimeter=80cm$

Therefore, The perimeter of each rectangle is $80cm$

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