Question

4 of 4 X a=6m, b=3m and c = 2 m for the triangle shown below. a b с Work out the value of x, giving your answer as an exact surd. The diagram is not drawn accurately x = 4√5 X m​

Answer 1

Answer: Therefore, the value of x is 4√5 meters.

Explanation:

To solve for x, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can see that side a is the hypotenuse, so we have:

a^2 = b^2 + c^2

Substituting the given values, we get:

(6m)^2 = (3m)^2 + (2m)^2

Simplifying:

36m^2 = 9m^2 + 4m^2

36m^2 = 13m^2

Dividing both sides by 13m^2:

36/13 = (4√5)^2/x^2

Simplifying:

x^2 = (4√5)^2 / (36/13)

x^2 = (16513) / 36

x^2 = 260/9

Taking the square root of both sides (and simplifying the surd):

x = 4√(65/9) = 4√5 X m