The height is 8 inches and the base is 22 inches
Step-by-step explanation:
The base of the triangle is six more than twice the height
The area of the triangle is 88 inches²
The area of any triangle is ⇒ A = [tex]\frac{1}{2}(b)(h)[/tex], wher b is its
base and h is its height
1. The base equals 6 + 2(height)
2. Its area is 88 inches²
3. Substitute the base in terms of the height , the height and the area
in the rule of the area to find the height
∵ The height of the triangle = h
∵ The base b = 6 + 2h
∵ A = 88 inches²
∵ A = [tex]\frac{1}{2}(b)(h)[/tex]
∴ 88 = [tex]\frac{1}{2}(6 + 2h)(h)[/tex]
∴ 88 = [tex](3 + h)(h)[/tex]
∴ 88 = 3h + h²
- Subtract 88 from both sides
∴ h² + 3h - 88 = 0
- Factorize it to find the value of h
∴ (h - 8)(h + 11) = 0
- Equate each bracket by 0
∴ h - 8 = 0 OR h + 11 = 0
∵ h - 8 = 0
- Add 8 to both sides
∴ h = 8 inches
∵ h + 11 = 0
- Subtract 11 from both sides
∴ h = -11 ⇒ we will ignore it because no negative value for the length
∵ b = 6 + 2h
- Substitute h by 8
∴ b = 6 + 2(8)
∴ b = 22 inches
The height is 8 inches and the base is 22 inches
Learn more:
You can learn more about the area of a triangle in brainly.com/question/4354581
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