Need URGENT HELP

Question

ABC is a triangular plot of land in which ACB is a right angle. The length of AB is (2x+1)m, the length of AC is (x–1)m and the length of BC is (2x–5)m. 

 

a) Using Pythagoras Theorem, form an equation in cans show that it reduces to x^2–26x+25=0

 

b) Solve x^2–26x+25=0

 

c) Calculate the area of triangle plot ABC

Answer 1

Part A)

 

 

AB is the hypotenuse

AC and BC are the two legs

 

Therefore, your equation using Pythagorean theorem is

 

(AC)² + (BC)² = (AB)²

 

(x - 1)² + (2x - 5)² = (2x + 1)²

 

 

Expand this equation to get

 

(x - 1)(x - 1) + (2x - 5)(2x - 5) = (2x + 1)(2x + 1)

 

(x² - 2x + 1) + (4x² - 20x + 25) = 4x² + 4x + 1

 

5x² - 22x + 26 = 4x² + 4x + 1

 

 

Make the left side equal to zero by bringing all terms to the left side.

 

x² - 26x + 25 = 0

 

 

 

Part B)

 

Solve the equation from part A.

 

We can factor the left side using FOIL.

 

(x - 25)(x - 1) = 0

 

 

Set the factors equal to zero.

 

x - 25 = 0             and                 x - 1 = 0

 

 

Solve for x from each equation.

 

x = 25              and               x = 1

 

 

Part C)

 

To calculate the area of the triangle, you need to get the actual side measures.  Since the algebraic expressions represent the side measures, substitute the accepted value of x into the equation.

 

x=1    makes AC a side measure a zero value.  So we accept x=25.

 

 

AC = x - 1

     = 25 - 1

     = 24 m

 

 

BC = 2(25) - 5

     = 50 - 5

     = 45 m

 

 

AB = 2(25) + 1

     = 50 + 1

     = 51

 

 

Checking into the Pythagorean theorem, we get

 

24²+ 45² = 51²

 

576 + 2025 = 2601

 

2601 = 2601

 

This checks out.  So now we multiply the measures of the legs and divide the result by 2.

 

Area = (AC * BC) / 2

 

 

Plug in the numbers to get the area.