Dear Friends, Please help on this problem :-
Cindy draws 3 Squares with different sizes. The sides of Square B is 3/5 the total sides of Square A and C. The sides of Square C is 1/7 of the total sides of Square A and B. if the area of Square A is 144sqcm, what is the total area of the 3 squares?
Apparently the sides are in the ratio
b = 3/5 (a+c)
c = 1/7 (a+b)
a^2 = 144
a,b,c = 12,9,3
so, area = 144+81+9 = 234
To find the total area of the three squares, we first need to determine the sides of Square B and Square C.
Let's start with Square B. We know that the sides of Square B are 3/5 the total sides of Square A and C. Since Square A's side length is unknown, we'll represent it by 'x'. Hence, the side length of Square B can be expressed as (3/5)x.
Moving on to Square C, we know that its side length is 1/7 of the total sides of Square A and B. Using the same representation as before, the side length of Square C is (1/7)x.
Now, we can find the areas of each square. The area of a square is calculated by squaring its side length.
Area of Square A = x^2 = 144 sq cm (given)
To find the areas of Square B and Square C, we'll need to calculate their side lengths first.
Area of Square B = (3/5)x * (3/5)x = (9/25)x^2
Area of Square C = (1/7)x * (1/7)x = (1/49)x^2
Now, we have the areas of all three squares. To find the total area, we need to sum up their individual areas.
Total Area = Area of Square A + Area of Square B + Area of Square C
= x^2 + (9/25)x^2 + (1/49)x^2
We can simplify this equation by finding a common denominator:
Total Area = (25/25)x^2 + (9/25)x^2 + (1/49)x^2
= (25x^2 + 9x^2 + x^2) / 25
Combining like terms:
Total Area = (35x^2) / 25
Since we know that the area of Square A is 144 sq cm, we can substitute x^2 with 144 to solve for the total area:
Total Area = (35 * 144) / 25
= 2016 / 25
= 80.64 sq cm
Therefore, the total area of the three squares is 80.64 square cm.