Respuesta :

This is a right triangle. We can demostrate it by applying the Pythagorean triple.

You get the hypothenuse (longest side) by the formula a²+b² = c²

So plug in the values. a and b are the legs and c the hypothenuse.

15²+20² = 25²

225+400 = 625

625 = 625

To find the hypothenuse square root the result.

c = √625 = 25 m

It is a right triangle.

Now, the area formula is: (l*l)/2 = (15*20)/2 = 300/2 = 150m²

The area of a triangle with legs that are 15 m, 25 m, and 20 m is [tex]150m^{2}[/tex]

Further Explanation;

Area  

  • Area is a measure of how much space is occupied by a given shape.
  • Area of a substance is determined by the type of shape in question.

For example;

  • Area of a rectangle is given by; Length multiplied by width
  • Area of a circle = πr². where r is the radius of a circle,
  • Area of a square = S², Where s is the side of the square.etc.

Area of a triangle  

  • The area of a triangle is given based on the type of the triangle in question.

Right triangle.

The area of a right triangle is given by;

                    =  1/2 x base x height

Scalene triangle

  • It is a triangle that with sides and angles that are not equal.
  • Area of a scalene triangle depends on the features of the triangle given.

For example;

Sine Formula

  • Area of a triangle = 1/2 ab sin θ, when given two sides of the triangle and the angle between them

Heron's formula

  • Area of a triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex] when given all the sides of the triangle.  

            where [tex]s =\frac{(a+b+c)}{2}[/tex]

In this case we are given, a = 15 m, b = 25 m, c = 20 m

Therefore, we use the Heron's formula;  

Area= [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]  

 [tex]s =\frac{(a+b+c)}{2}[/tex]

[tex]s= \frac{(15+25+20)}{2} \\s= 30[/tex]

Therefore;

Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]  

       = [tex]30\sqrt{30(30-15)(30-25)(30-20)}[/tex]  

       =[tex]\sqrt{30(15)(5)(10)} \\\sqrt{22500}[/tex]

[tex]= 150m^{2}[/tex]

Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.

Learn more about:

  • Perimeter: https://brainly.com/question/12905000
  • Area: https://brainly.com/question/12905000
  • Area of a triangle: https://brainly.com/question/4354581
  • Heron's Formula: https://brainly.com/question/4354581
  • Sine Formula: https://brainly.com/question/4354581

Level: Middle school

Subject; Mathematics  

Topic: Area  

Sub-topic: Area of a triangle  

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