Mathematics Question and Solution
Calculating The Shaded Area.
Let x be the three equal lengths.
a²+x² = 5²
a = √(25-x²) units.
a is the height of the ascribed right-angled triangle.
Calculating x
a ~ x
2x ~ x
Cross Multiply.
ax = 2x²
2x = a. And a = √(25-x²) units.
2x = √(25-x²)
4x² = 25-x²
5x² = 25
x = √(5) units.
Recall.
a = √(25-x²) units.
a = √(25-√(5)²)
a = √(20) units.
a = 2√(5) units.
b = 2x
b = 2√(5) units.
It implies;
Shaded Area is;
½(2√(5)*2√(5))-½(√(5)*2√(5))-½(√(5)*√(5))
= ½(20)-½(10)-½(5)
= ½(20-10-5)
= ½(5) square units.
= 2.5 square units.
Or
Shaded Area is;
½*√(5)*√(5)
= ½(5)
= 2.5 square units.
