The distance between the A to E is 13 units if the area of square ABCD is 100, the area of triangle DEC is 10,
What is the Pythagoras theorem?
The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
From the figure:
Each side length of the square is 10 units (because the area of the square is 100 square units)
XY = 10 units
Area of the triangle = (1/2)height×base length
10 = (1/2)EX(10)
EX = 2 units
So from the right angle triangle:
ΔAEY:
EY = EX + XY = 2 + 10 = 12 units
AY = 10/2 = 5 units
AE = √(EY² + AY²)
AE = √(12² + 5²)
AE = 13 units
Thus, the distance between the A to E is 13 units if the area of square ABCD is 100, the area of triangle DEC is 10,
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