Solution:
Let the legs be 8x and 15x.
The hypotenuse is 6.8 cm long.
Using Pythagoras theorem we can write
[tex](8x)^2+(15x)^2=(6.8)^2\\ \\ 64x^2+225x^2=(6.8)^2\\ \\ 289x^2=(6.8)^2\\ \\ 17x=6.8\\ \\ x=0.4\\[/tex]
So the legs are
[tex]8x=8*0.4=3.2\\ \\ 15x=15*0.4=6\\[/tex]
Are of Triangle[tex]=\frac{1}{2}base*height\\[/tex]
Are of Triangle[tex]=\frac{1}{2}3.2*6=9.6cm^2\\[/tex]
The area of the triangle is 9.60 cm².
A right triangle is a triangle that is made up of a hypotenuse, base and height. One of the angles in this triangle is 90 degrees.
The area of a right triangle = 1/2 x base x height
The values of the base and height have to be determined. The Pythagoras theorem would be used to determine these values.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
8x² + 15x² = 6.8²
64x² + 225x² = 6.8²
289x² = 6.8²
Find the square root of both sides
17x = 6.8
x = = 6.8 / 17
x = 0.4
Base = 8x = 8 x 0.4 = 3.2 cm
Height = 15x = 0.4 x 15 = 6 cm
Area of the triangle = 1/2 x 3.2 x 6 = 9.60 cm²
To learn more about Pythagoras theorem, please check: brainly.com/question/20936855
