Answer:
Segment AD is 3, and segment AE is 2.
Step-by-step explanation:
In a triangle, the line joining the mid points of two sides is parallel and half of the third sides of the triangle.
Here, ABC is a triangle,
In which,
AB = 6,
AC = 4,
D∈ AB and E∈AC
Let DE ║BC,
And, ![DE=\frac{1}{2}BC](https://tex.z-dn.net/?f=DE%3D%5Cfrac%7B1%7D%7B2%7DBC)
In triangles ADE and ABC,
( Alternative interior angle theorem )
![\angle AED\cong \angle ACB](https://tex.z-dn.net/?f=%5Cangle%20AED%5Ccong%20%5Cangle%20ACB)
By AA similarity postulate,
![\triangle ADE\sim \triangle ABC](https://tex.z-dn.net/?f=%5Ctriangle%20ADE%5Csim%20%5Ctriangle%20ABC)
∵ Corresponding sides of similar triangle are in same proportion,
![\implies \frac{AD}{AB}=\frac{AE}{AC}=\frac{DE}{BC}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7BAD%7D%7BAB%7D%3D%5Cfrac%7BAE%7D%7BAC%7D%3D%5Cfrac%7BDE%7D%7BBC%7D)
![\frac{AD}{AB}=\frac{AE}{AC}=\frac{BC}{2BC}](https://tex.z-dn.net/?f=%5Cfrac%7BAD%7D%7BAB%7D%3D%5Cfrac%7BAE%7D%7BAC%7D%3D%5Cfrac%7BBC%7D%7B2BC%7D)
![\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7BAD%7D%7BAB%7D%3D%5Cfrac%7BAE%7D%7BAC%7D%3D%5Cfrac%7B1%7D%7B2%7D)
![\implies AD = \frac{AB}{2}\text{ and }AE =\frac{AC}{2}](https://tex.z-dn.net/?f=%5Cimplies%20AD%20%3D%20%5Cfrac%7BAB%7D%7B2%7D%5Ctext%7B%20and%20%7DAE%20%3D%5Cfrac%7BAC%7D%7B2%7D)
![\implies AD = \frac{6}{2}=3\text{ and }AE =\frac{4}{2}=2](https://tex.z-dn.net/?f=%5Cimplies%20AD%20%3D%20%5Cfrac%7B6%7D%7B2%7D%3D3%5Ctext%7B%20and%20%7DAE%20%3D%5Cfrac%7B4%7D%7B2%7D%3D2)
Hence, the correct option would be,
Segment AD is 3, and segment AE is 2.
Answer:
x= -5/3 y-5
Step-by-step explanation:
Answer:
x = 6
a = 18 ft
b = 36 ft
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
- Factoring/Expanding
- Solving quadratics
<u>Trigonometry</u>
- Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Define</u>
Given: Right triangle
a = 3x
b = 6x
c = 40
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute: (3x)² + (6x)² = 40²
- Evaluate: 9x² + 36x² = 1600
- Combine like terms: 45x² = 1600
- Isolate <em>x </em>term: x² = 320/9
- Isolate <em>x</em>: x = (±8√5)/3
- Evaluate: x = ±5.96285
Since it is not a quadrant triangle, we must use the positive value for <em>x</em>.
<u>Step 3: Find legs</u>
Leg a
- Define: 3x
- Substitute: 3(5.96285)
- Multiply: 17.8885
- Round: 18
Leg b
- Define: 6x
- Substitute: 6(5.96285)
- Multiply: 35.7771
- Round: 36
The answer is 8 hope this helps :)
Answer:
the answer is debt
Step-by-step explanation: