sum of the areas of two squares is 850 m square if the difference of their perimeter is 40 m. find the sides of the two squares
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Perimeter of a square = 4L since all the sides are equal.
Let the smaller square be of side x.
Since the difference in perimeter = 40 m then each side of the larger square is greater by:
= 40/4 = 10 m
The sides of the larger square will be (x + 10) m
Their areas are as follows :
x² + (x + 10)² = 850
Expanding this we have :
x² + x² + 20x + 100 = 850
Collecting the like terms together we have :
2x² + 20x - 750 = 0
Divide all through by 2 we have :
x² + 10x - 375 = 0
The roots are +25 and - 15
We expand the equation :
x² + 25x - 15x - 375 = 0
x(x + 25) - 15(x + 25) = 0
(x - 15)(x + 25) = 0
The value of x will be :
x = 15 or - 25
We take the positive value of x since measurements are normally positive.
The side of the bigger side is :
15 + 10 = 25
Smaller square : 15 by 15
Bigger square = 25 by 25