#1**+2 **

we can use the pythagorenas theorem to find the altitude is 60 and we have te equation 60^2+x^2=y^2 and (x+25)^2-65^2=y^2 where y is the base

jimkey17 Jul 11, 2020

#2**+1 **

In the small right triangle on the RHS with sides of 65 and 25, wil find the altitude by Pythagoras's Theorem:

65^2 =25^2 + A^2

A =sqrt(3600) =60

The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the **geometric mean** of the measures of the two segments of the hypotenuse.

Sqrt(25x) =60

5sqrt(x) =60 Divide both sides by 5

sqrt(x) =12 Square both sides

**x = 144**

Guest Jul 11, 2020

#4**0 **

I think Alan made a typo. You can't solve for x in the last equation!

Cos(25/65) = 65 /(x + 25) - Now you can solve for x

169 =x + 25

**x =169 - 25 = 144**

Guest Jul 11, 2020

#6**0 **

Hello, Guest!

Alan's equation is solvable; it just takes more time, but the result is the same.

65 / x+25 = 25 / 65

Step 1: Cross-multiply.

65 * 65 = 25 * x+25

4225 = 25x + 625

Step 2: Flip the equation.

25x + 625 = 4225

Step 3: Subtract 625 from both sides.

25x + 625−625 = 4225−625

25x = 3600

Step 4: Divide both sides by 25.

25x / 25 = 3600 / 25

x = 144

Guest Jul 11, 2020