Question

Please help me with this homework question. No silly answers please and no bots! I will mark brainliest to whoever gets all them right. Thank you !​

Answer 1

Answer:

The formula for the area of the triangle is:

$\displaystyle A=24x^2$

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:

$\displaystyle A=\frac{1}{2}bh$

So, by substitution:

$\displaystyle A=\frac{1}{2}(8x)(6x)=24x^2$

When x = 3, the area will be:

$\displaystyle A(3)=24(3)^2=216\text{ cm}^2$

And when x = 2.4, the area will be:

$A(2.4)=24(2.4)^2=138.24\text{ cm}^2$

When x = 5, the height will be 8(5) = 40 cm and the base will be 6(5) = 30 cm.

By the Pythagorean Theorem:

$a^2+b^2=c^2$

So:

$(40)^2+(30)^2=c^2$

The hypotenuse will be:

$c=\sqrt{1600+900}=\sqrt{2500}=50\text{ cm}$