Answer:
a = 25m^2
b = 5m
d = 35.73 m^2
c = 7.94m
Explanation:
First, remember that the area of a square of side length L is:
A = L^2
And for a triangle rectangle with catheti a and b, and hypotenuse H, we have the relation:
H^2 = a^2 + b^2 (Phytagorean's theorem)
Ok, let's look at the left image, we have a green triangle rectangle.
The bottom cathetus has a length equal to the side length of a square with area of 16m^2
Then the side length of that square (and the cathetus) is:
L^2 = 16m^2
L = √(16m^2) = 4m
The left cathetus has a length equal to the side length of a square of area = 9m^2
Then the side length of that cathetus is:
K^2 = 9m^2
K = √(9m^) = 3m
Then the catheti of the green triangle rectangle are:
4m and 3m
Then the hypotenuse of this triangle (b) is:
b^2 = (4m)^2 + (3m)^2
b^2 = 16m^2 + 9m^2 = 25m^2
b = √(25m^2) = 5m
And b is the side length of the red square, then the area of that square is:
a = b^2 = 25m^2
Now let's go to the other image.
Here we have an hypotenuse of side length H, such that:
H^2 = 144m^2
And we have a cathetus (the one adjacent to the green triangle) of side length L such that:
L^2 = 81m^2
The other cathetus will have a sidelength c, such that:
c^2 = area of the purple square
By the Pythagorean's theorem we have:
144m^2 = 81m^2 + c^2
144m^2 = 81m^2 + c^2
144m^2 - 81m^2 = c^2
63m^2 = c^2
(√63m^2) = c = 7.94m
And the area of a triangle rectangle is equal to the product between the catheti divided by two.
We know that one cathetus is equal to c = 7.94m
And the other on is equal to the square root of 81m^2
√(81m^2) = 9m
then the area of the triangle is:
d = (7.94m)*(9m)/2 = 35.73 m^2