Solved on Nov 03, 2023

Find the value of $x$ such that $\angle A = 60^\circ$ in a triangle $ABC$ with $AB = 6x - 3$ and $BC = 4x + 9$ , where $B$ is the midpoint of $AC$ .

STEP 1

Assumptions1. Triangle ABC is given, with angle A being60 degrees. . Point B is the midpoint of line segment AC.
3. The lengths are given as AB=6x-3 and BC=4x+9.
4. We need to find the value of 'x' such that A=60.

STEP 2

Since B is the midpoint of AC, the triangle ABC is an isosceles triangle (AB = BC).

STEP 3

Set the lengths of AB and BC equal to each other because they are equal in an isosceles triangle.
$6x-3 =x+9$

STEP 4

Rearrange the equation to isolate x terms on one side and constants on the other.
$6x -4x =9 +3$

STEP 5

implify the equation to find the value of x.
$2x =12$

STEP 6

Divide both sides of the equation by2 to solve for x.
$x =12 /2$

STEP 7

Calculate the value of x.
$x =12 /2 =6$ The value of 'x' such that A=60 is6.

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Find the value of $x$ such that $\angle A = 60^\circ$ in a triangle $ABC$ with $AB = 6x - 3$ and $BC = 4x + 9$ , where $B$ is the midpoint of $AC$ .

STEP 1

Assumptions1. Triangle ABC is given, with angle A being60 degrees. . Point B is the midpoint of line segment AC.
3. The lengths are given as AB=6x-3 and BC=4x+9.
4. We need to find the value of 'x' such that A=60.

STEP 2

Since B is the midpoint of AC, the triangle ABC is an isosceles triangle (AB = BC).

STEP 3

Set the lengths of AB and BC equal to each other because they are equal in an isosceles triangle.
$6x-3 =x+9$

STEP 4

Rearrange the equation to isolate x terms on one side and constants on the other.
$6x -4x =9 +3$

STEP 5

implify the equation to find the value of x.
$2x =12$

STEP 6

Divide both sides of the equation by2 to solve for x.
$x =12 /2$

STEP 7

Calculate the value of x.
$x =12 /2 =6$ The value of 'x' such that A=60 is6.

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Find the value of xxx such that ∠A=60∘\angle A = 60^\circ∠A=60∘ in a triangle ABCABCABC with AB=6x−3AB = 6x - 3AB=6x−3 and BC=4x+9BC = 4x + 9BC=4x+9, where BBB is the midpoint of ACACAC.

STEP 1

Assumptions1. Triangle ABC is given, with angle A being60 degrees. . Point B is the midpoint of line segment AC.3. The lengths are given as AB=6x-3 and BC=4x+9.4. We need to find the value of 'x' such that A=60.

STEP 2

Since B is the midpoint of AC, the triangle ABC is an isosceles triangle (AB = BC).

STEP 3

Set the lengths of AB and BC equal to each other because they are equal in an isosceles triangle.6x−3=x+96x-3 =x+96x−3=x+9

STEP 4

Rearrange the equation to isolate x terms on one side and constants on the other.6x−4x=9+36x -4x =9 +36x−4x=9+3

STEP 5

implify the equation to find the value of x.2x=122x =122x=12

STEP 6

Divide both sides of the equation by2 to solve for x.x=12/2x =12 /2x=12/2

STEP 7

Calculate the value of x.x=12/2=6x =12 /2 =6x=12/2=6The value of 'x' such that A=60 is6.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the value of $x$ such that $\angle A = 60^\circ$ in a triangle $ABC$ with $AB = 6x - 3$ and $BC = 4x + 9$ , where $B$ is the midpoint of $AC$ .

Assumptions1. Triangle ABC is given, with angle A being60 degrees. . Point B is the midpoint of line segment AC.
3. The lengths are given as AB=6x-3 and BC=4x+9.
4. We need to find the value of 'x' such that A=60.

Set the lengths of AB and BC equal to each other because they are equal in an isosceles triangle.
$6x-3 =x+9$

Rearrange the equation to isolate x terms on one side and constants on the other.
$6x -4x =9 +3$

implify the equation to find the value of x.
$2x =12$

Divide both sides of the equation by2 to solve for x.
$x =12 /2$

Calculate the value of x.
$x =12 /2 =6$ The value of 'x' such that A=60 is6.