Question

The perimeter of the triangle BAG is 43. AG= 16, AB=x+4, and BG= 2x+2. What is the value of x?

Answer 1

x=7

isosceles triangle

Explanation:

To find the perimeter we just add all the sides so we do that for this too

(X+4)+(2x+2)+(16)

And we set it equal to 43 since that is perimeter

(X+4)+(2x+2)+(16)=43

Combine like terms

3x+22=43

-22. -22

3x=21

/3. /3

x=7

And if we fill in the x we find BG and AG are equal so this is an Isosceles triangle

Hopes this helps

Answer 2

x = 7

Isosceles triangle

Explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Given values of triangle BAG:

• Perimeter = 43
• AG = 16
• AB = x + 4
• BG = 2x + 2

Therefore:

⇒ AG + AB + BG = perimeter

⇒ 16 + x + 4 + 2x + 2 = 43

⇒ x + 2x + 16 + 4 + 2 = 43

⇒ 3x + 22 = 43

⇒ 3x + 22 - 22 = 43 - 22

⇒ 3x = 21

⇒ 3x ÷ 3 = 21 ÷ 3

⇒ x = 7

Substitute the found value of x into the expressions for AB and BG to find their lengths:

⇒ AB = x + 4

⇒ AB = 7 + 4

⇒ AB = 11

⇒ BG = 2x + 2

⇒ BG = 2(7) + 2

⇒ BG = 14 + 2

⇒ BG = 16

As sides BG and AG are both 16 units in length, the triangle is an isosceles triangle (as it has two sides of equal length).