The sum of the areas of two squares is 41 Sq. cm. If the sum of their perimeter is 36 cm. then find the side of the two squares.
Answers
Given : The sum of the areas of two squares is 41 Sq. cm.
sum of their perimeter is 36 cm.
To find : side of the two squares.
Solution:
side of the two squares. = x & y
Square with side x
Perimeter = 4x
Area = x²
Square with side y
Perimeter = 4y
Area = y²
sum of their perimeter is 36 cm.
=> 4x + 4y = 36
=> x + y = 9
=> y = 9 - x
sum of the areas of two squares is 41 Sq. cm
=> x² + y² = 41
=> x² + (9 - x)² = 41
=> x² + 81 + x² - 18x = 41
=> 2x² - 18x + 40 = 0
=> x² - 9x + 20 = 0
=> x² - 4x - 5x + 20 = 0
=> (x - 4)(x - 5) = 0
=> x = 4 or x = 5
=> y = 5 or y = 4
side of the two squares are 4 cm and 5 cm
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