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Answer :
Final answer:
The area of the triangle with legs 15 m, 25 m, and 20 m is 187.5 m².
Explanation:
To find the area of a triangle, we can use the formula: Area = (base * height) / 2.
In this case, the legs of the triangle can be considered as the base and height. Let's take the legs as 15 m and 25 m.
Substituting the values into the formula:
Area = (15 m * 25 m) / 2
Area = 375 m² / 2
Area = 187.5 m²
Therefore, the area of the triangle is 187.5 m².
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Rewritten by : Jeany
The area of the triangle with legs of lengths 15 m, 25 m, and 20 m is 150 m², which corresponds to option B.
To find the area of a triangle given the lengths of its legs, we can use Heron's formula. Heron's formula states that the area (A) of a triangle with side lengths [tex]\(a\), \(b\)[/tex], and [tex]\(c\)[/tex] can be calculated using the semi-perimeter [tex](\(s\))[/tex] of the triangle, which is half the perimeter, as follows:
[tex]\[A = \sqrt{s(s - a)(s - b)(s - c)}\][/tex]
Where [tex]\(s = \frac{a + b + c}{2}\).[/tex]
Given the lengths of the legs of the triangle:
[tex]\(a = 15 \, \text{m}\)[/tex]
[tex]\(b = 25 \, \text{m}\)[/tex]
[tex]\(c = 20 \, \text{m}\)[/tex]
First, let's calculate the semi-perimeter [tex](\(s\)):[/tex]
[tex]\[s = \frac{a + b + c}{2}\][/tex]
[tex]\[s = \frac{15 + 25 + 20}{2}\][/tex]
[tex]\[s = \frac{60}{2}\][/tex]
[tex]\[s = 30 \, \text{m}\][/tex]
Now, let's plug the values into Heron's formula:
[tex]\[A = \sqrt{30(30 - 15)(30 - 25)(30 - 20)}\][/tex]
[tex]\[A = \sqrt{30 \times 15 \times 5 \times 10}\][/tex]
[tex]\[A = \sqrt{22500}\][/tex]
[tex]\[A = 150 \, \text{m}^2\][/tex]
So, the area of the triangle is [tex]\(150 \, \text{m}^2\)[/tex], which corresponds to option B.
