Question

the longest side of a right angled triangle is 125 m and one of the remaining two side is 100m.. find its area

Answer 1

The area of the triangle is 3750 m²

Explanation:

• The formula of the area of a right triangle is A =
  `(1)/(2)` 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 =
  `\sqrt{b^(2)+h^(2)}`

∵ 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 =
`\sqrt{b^(2)+h^(2)}`

∴ 125 =
`\sqrt{100^(2)+h^(2)}`

- Square the two sides

∴ 15625 = 10000 + h²

- Subtract 10000 from both sides

∴ 5625 = h²

- Take √ for both sides

∴ 75 = h

∴ h = 75 m

∵ A =
`(1)/(2)` bh

- Substitute the values of b and h in the formula above

∴ A =
`(1)/(2)` (100)(75)

∴ A = 3750

∴ The area of the triangle is 3750 m²