there is a large square portrait of a leader covers an area of 4489cm square. if each side has a 2cm liner ,what would be its area?
Answers
The area of the portrait is 3969 cm².
• Given data :
The total area of the portrait including the liner is 4489 cm².
The thickness of the liner is 2 centimetres.
• Let,the side of the portrait = x centimetres ( assume x as a variable to calculate the total area of the potrait)
• So,the length of one side of the potrait including the liner is
= {x+(2×2)} (×2 because the width of the liners are added in both sides of length)
= x+4 cm²
• So,the area of the potrait including liners
= (x+4)² cm²
• Now, if we compare the value of the total area that we calculated and the value of the total area given in the question,we will get the following equation :
(x+4)²= 4489
x+4 = 67
x = 67-4
x = 63
So,the length of the one side of the portrait is 63 centimetres.
So,the area of the potrait = (63)²
= 3969 cm² (answer)