Question

ABCD is a square formed by 4 identical rectangles. The Perimeter of each rectangle is 80cm. How long is AB?

Answer 1

${\large{\bold{\rm{\underline{\underbrace{Understanding \; the \; question}}}}}}$

❖ This question says that ABCD is a square and it is formed by 4 identical rectangles. And it's also given that the perimeter of each rectangle is 80 cm. We have to find that what is the length of AB means how long the line AB is (Diagram of this question is given in attachment).

${\large{\bold{\rm{\underline{Given \; that}}}}}$

❖ ABCD is a square

❖ Given square is formed by 4 identical rectangles

❖ Perimeter of each rectangle = 80 cm

${\large{\bold{\rm{\underline{To \; find}}}}}$

❖ Length of AB.

${\large{\bold{\rm{\underline{Solution}}}}}$

❖ Length of AB = 32 cm

${\large{\bold{\rm{\underline{Using \; concept}}}}}$

❖ Formula to find perimeter of rectangle

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

❖ Perimeter of rectangle = 2(l+b)

${\large{\bold{\rm{\underline{Where,}}}}}$

★ l denotes length

★ b denotes breadth

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ As in the question it's already given that ABCD is a square and it is formed by 4 identical rectangles so according to this new formed equation is,

~ The length of the rectangle is equals to 4 times to it's breadth.

• l = 4b

In short the value of length is 4 cm

Means,

• 2(4b+1b)

Let's solve this,

• 2(4b+1b)

• 2(5b)

• 10b

~ As it's already given that perimeter of each of the rectangle is 80. So, according to this,

• 10b = 80

• b = 80/10

• b = 8

In short value of breadth is 8 cm

~ According to the question,

• Length = 4 cm

• Breadth = 8 cm

• Length = 4 × 8

• Length = 32 cm