Question

A right-angled triangle has sides of lenghts (x+5)cm, (x-3)cm and 9cm with the angle of side 9cm being the hypotenuse. Calculate the value of x and give your answer to 3 significant figures.

Answer 1

To find the value of x in the right-angled triangle, we can use the Pythagorean theorem and solve the resulting equation. The value of x is approximately 4.783.

Step-by-step explanation:

To find the value of x, we can use the Pythagorean theorem.

According to the theorem, the sum of the squares of the lengths of the two legs of a right-angled triangle is equal to the square of the length of the hypotenuse.

In this case, we have the equation

(x+5)² + (x-3)² = 9².

Expanding the equation, we get

x² + 10x + 25 + x² - 6x + 9 = 81.

Combining like terms and solving for x, we get x² + 4x - 47 = 0.

Using the quadratic formula, we find x ≈ 4.783.