Question

A right triangle has legs with lengths equal to 10 inches and 9x inches. Its hypotenuse measures (x + 10) inches. What is the approximate value of the hypotenuse? 10 inches 10.25 inches 20.25 inches 81 inches

Answer 1

Answer:

10.25 inches

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:

${h}^{2} = {p}^{2} + {b}^{2}$

Plug the values

${(x + 10)}^{2} = {(9x)}^{2} + {(10)}^{2}$

Using ${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$ , expand the expression

${x}^{2} + 20x + 100 = {(9x)}^{2} + {10}^{2}$

To raise a product to a power , raise each factor to that power

${x}^{2} + 20x + 100 = 81 {x}^{2} + {10}^{2}$

Evaluate the power

${x}^{2} + 20x + 100 = 81 {x}^{2} + 100$

Cancel equal terms on both sides of the equation

${x}^{2} + 20x = 81 {x}^{2}$

Move x² to R.H.S and change its sign

$20x = 81 {x}^{2} - {x}^{2}$

Calculate

$20x = 80 {x}^{2}$

Swap both sides of the equation and cancel both on both sides

$80x = 20$

Divide both sides of the equation by 80

$\frac{80x}{80} = \frac{20}{80}$

Calculate

$x = \frac{20}{80}$

Reduce the numbers with 20

$x = \frac{1}{4}$

The value of X is $\frac{1}{4}$

Now, let's replace the value of x to find the approximate value of hypotenuse

Hypotenuse = $\frac{1}{4} + 10$

Write all numerators above the common denominator

$\frac{1 + 40}{4}$

Add the numbers

$\frac{41}{4}$

$= 10.25$ inches

Hope this helps..

best regards!!

Answer 2

Answer:

10.25

Step-by-step explanation:

because I said so ya skoozie