Right Triangle

Question

The measures of the legs of a right triangle can be represented by the expressions 3(x^4)(y) and 2 (x^4)(y).

 

a. What is the area of the triangle?

b. What is the measure of the hypotenuse?

c. What is the perimeter of the triangle?

Answer 1

For a right triangle, the two sides of the triangle that are perpendicular to each other are the base and the height of the triangle.  In this case, the two legs of the right triangle are perpendicular to each other so they are the base and the height of the triangle.

 

The formula for the area of a triangle is (1/2)bh, where b is the base and h is the height. So the area is:

 

(3x⁴y)(2x⁴y) / 2 = 3x⁸y²

 

To find the measure of the hypotenuse, use Pythagorean Theorem formula:  hypot² = b² + h²

 

hypot² = (3x⁴y)² + (2x⁴y)²

hypot² = 9x⁸y² + 4x⁸y²

hypot² = 13x⁸y²  (Now take the square root of both sides of the equation.)

 

hypot = x⁴y√13

 

To find the perimeter of the triangle, add up all three lengths.

 

x⁴y√13 + 3x⁴y + 2x⁴y  (Factor out x⁴y.)

 

x⁴y(√13 + 3 + 2)

 

x⁴y(5 + √13)

 

 

Answer 2

a. 3x⁸y²

b. x⁴y√13

c. 5x⁴y + x⁴y√13