Answer:
The area of the triangle is 3750 m²
Step-by-step explanation:
- The formula of the area of a right triangle is A = [tex]\frac{1}{2}[/tex] bh, where b and h are the legs of the right angle
- The longest side in the right triangle is the side opposite to the right angle and is called the hypotenuse
- The length of the hypotenuse = [tex]\sqrt{b^{2}+h^{2}}[/tex]
∵ The longest side of a right angled triangle is 125 m
∴ the length of the hypotenuse = 125 m
∵ The length of one of the remaining two side is 100 m
∴ b = 100 m
To find the area of the triangle you must find the other side of the right angle
∵ The length of the hypotenuse = [tex]\sqrt{b^{2}+h^{2}}[/tex]
∴ 125 = [tex]\sqrt{100^{2}+h^{2}}[/tex]
- Square the two sides
∴ 15625 = 10000 + h²
- Subtract 10000 from both sides
∴ 5625 = h²
- Take √ for both sides
∴ 75 = h
∴ h = 75 m
∵ A = [tex]\frac{1}{2}[/tex] bh
- Substitute the values of b and h in the formula above
∴ A = [tex]\frac{1}{2}[/tex] (100)(75)
∴ A = 3750
∴ The area of the triangle is 3750 m²
