Answer:
<h2>
10.25 inches</h2>
Step-by-step explanation:
Given,
Perpendicular ( p ) = 9x
Base ( b ) = 10
Hypotenuse ( h ) = x + 10
Now, let's find the value of x
Using Pythagoras theorem:
![{h}^{2} = {p}^{2} + {b}^{2}](https://tex.z-dn.net/?f=%20%7Bh%7D%5E%7B2%7D%20%20%3D%20%20%7Bp%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20)
Plug the values
![{(x + 10)}^{2} = {(9x)}^{2} + {(10)}^{2}](https://tex.z-dn.net/?f=%20%7B%28x%20%2B%2010%29%7D%5E%7B2%7D%20%20%3D%20%20%7B%289x%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%2810%29%7D%5E%7B2%7D%20)
Using
, expand the expression
![{x}^{2} + 20x + 100 = {(9x)}^{2} + {10}^{2}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%2020x%20%2B%20100%20%3D%20%20%7B%289x%29%7D%5E%7B2%7D%20%20%2B%20%20%7B10%7D%5E%7B2%7D%20)
To raise a product to a power , raise each factor to that power
![{x}^{2} + 20x + 100 = 81 {x}^{2} + {10}^{2}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%2020x%20%2B%20100%20%3D%2081%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7B10%7D%5E%7B2%7D%20)
Evaluate the power
![{x}^{2} + 20x + 100 = 81 {x}^{2} + 100](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%2020x%20%2B%20100%20%3D%2081%20%7Bx%7D%5E%7B2%7D%20%20%2B%20100)
Cancel equal terms on both sides of the equation
![{x}^{2} + 20x = 81 {x}^{2}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%2020x%20%3D%2081%20%7Bx%7D%5E%7B2%7D%20)
Move x² to R.H.S and change its sign
![20x = 81 {x}^{2} - {x}^{2}](https://tex.z-dn.net/?f=20x%20%3D%2081%20%7Bx%7D%5E%7B2%7D%20%20-%20%20%7Bx%7D%5E%7B2%7D%20)
Calculate
![20x = 80 {x}^{2}](https://tex.z-dn.net/?f=20x%20%3D%2080%20%7Bx%7D%5E%7B2%7D%20)
Swap both sides of the equation and cancel both on both sides
![80x = 20](https://tex.z-dn.net/?f=80x%20%3D%2020)
Divide both sides of the equation by 80
![\frac{80x}{80} = \frac{20}{80}](https://tex.z-dn.net/?f=%20%5Cfrac%7B80x%7D%7B80%7D%20%20%3D%20%20%5Cfrac%7B20%7D%7B80%7D%20)
Calculate
![x = \frac{20}{80}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B20%7D%7B80%7D%20)
Reduce the numbers with 20
![x = \frac{1}{4}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20)
The value of X is ![\frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20)
Now, let's replace the value of x to find the approximate value of hypotenuse
Hypotenuse = ![\frac{1}{4} + 10](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20%20%2B%2010)
Write all numerators above the common denominator
![\frac{1 + 40}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%20%2B%2040%7D%7B4%7D%20)
Add the numbers
![\frac{41}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B41%7D%7B4%7D%20)
inches
Hope this helps..
best regards!!