The areas of the squares adjacent to two sides of a right triangle are 32units^2 and 32 units^2. Find the length, x, of the third side of the triangle.

The length of the third side of the triangle is 8 units

Step-by-step explanation:

Here, since the two sides are adjacent a square, what this means is that the length of the square equals the length of the sides of the triangle adjacent to it.

Mathematically, the formula for the area of a square is L^2

With an area of 32 square units, the length of the side of this triangle is thus √(32) =

4√2 units

So we have two sides of the right triangle with length 4√2 units

Now we should know that this right triangle is an isosceles right triangle since the lengths of the adjacent and the opposite are equal.

Now to calculate the length of the third side which is the hypotenuse, we make use of the pythagoras’ theorem which states that the square of the longest side of a right triangle which is the hypotenuse is equal to the sum of the squares of the other two sides

Thus mathematically, the square of the hypotenuse length is 32 + 32 = 64

Let’s call the hypotenuse h for documentation purposes

h^2 = 64

h = √64

h = 8 units

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places