Answer :
The area of a triangle with legs of 15m, 25m, and 20m is 150m² when calculated using the formula for the area of a triangle.
The area of a triangle is calculated using the formula:
Area = 1/2 × base × height
Given a triangle with legs 15 m, 25 m, and 20 m, we need to find the area. To do this, we first need to determine the base and height of the triangle.
Let's consider the sides of 15 m and 20 m as the base and height, respectively. Plug these values into the formula to find the area of the triangle.
Area = 1/2 × 15 m × 20 m = 150 m²
Therefore, the area of the triangle with legs 15 m, 25 m, and 20 m is 150 m².
The area of a triangle is 150 m²
The correct option is (b).
To find the area of a triangle given the lengths of its three sides (often referred to as Heron's formula), we can use the following steps:
1. Calculate the semi-perimeter (s) of the triangle using the formula:
[tex]\( s = \frac{a + b + c}{2} \)[/tex]
where [tex]\( a \), \( b \), and \( c \)[/tex] are the lengths of the sides.
2. Calculate the area (A) using Heron's formula:
[tex]\( A = \sqrt{s \cdot (s - a) \cdot (s - b) \cdot (s - c)} \)[/tex]
Given the lengths of the sides as 15 m, 25 m, and 20 m, we can plug these values into the formulas.
1. Calculate the semi-perimeter:
[tex]\( s = \frac{15 + 25 + 20}{2} \)[/tex]
[tex]\( s = \frac{60}{2} \)[/tex]
[tex]\( s = 30 \)[/tex] m
2. Calculate the area using Heron's formula:
[tex]\( A = \sqrt{30 \cdot (30 - 15) \cdot (30 - 25) \cdot (30 - 20)} \)[/tex]
[tex]\( A = \sqrt{30 \cdot 15 \cdot 5 \cdot 10} \)[/tex]
[tex]\( A = \sqrt{22500} \)[/tex]
[tex]\( A = 150 \) m²[/tex]
So, the correct answer is b) 150 m².