Answer:
The formula for the area of the triangle is:
[tex]\displaystyle A=24x^2[/tex]
When x = 3, the area is 216 square centimeters.
When x = 2.4, the area is 138.24 square centimeters.
And when x = 5, the hypotenuse of the triangle is 50 centimeters.
Step-by-step explanation:
We are given a right triangle with a height of 8x and a base of 6x.
The area of a triangle is given by the formula:
[tex]\displaystyle A=\frac{1}{2}bh[/tex]
So, by substitution:
[tex]\displaystyle A=\frac{1}{2}(8x)(6x)=24x^2[/tex]
When x = 3, the area will be:
[tex]\displaystyle A(3)=24(3)^2=216\text{ cm}^2[/tex]
And when x = 2.4, the area will be:
[tex]A(2.4)=24(2.4)^2=138.24\text{ cm}^2[/tex]
When x = 5, the height will be 8(5) = 40 cm and the base will be 6(5) = 30 cm.
By the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
So:
[tex](40)^2+(30)^2=c^2[/tex]
The hypotenuse will be:
[tex]c=\sqrt{1600+900}=\sqrt{2500}=50\text{ cm}[/tex]
