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Answer :
To solve this problem, you need to find which equation can be used to determine the value of [tex]\( x \)[/tex] in an isosceles triangle where the perimeter is 7.5 meters, and the shortest side [tex]\( y \)[/tex] is 2.1 meters.
### Step-by-step Solution
1. Understand the triangle properties:
- An isosceles triangle has two sides that are equal in length. Let’s assume these two equal sides are each [tex]\( x \)[/tex].
- The shortest side is given as [tex]\( y = 2.1 \)[/tex] meters.
2. Formula for Perimeter:
- The formula for the perimeter [tex]\( P \)[/tex] of an isosceles triangle is:
[tex]\[
P = x + x + y = 2x + y
\][/tex]
- Substituting the given perimeter and the shortest side ([tex]\( y = 2.1 \)[/tex]):
[tex]\[
7.5 = 2x + 2.1
\][/tex]
3. Solve the equation for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( 2x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Simplify the equation:
[tex]\[
2x = 5.4
\][/tex]
- Divide by 2 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
4. Check the options:
- Option 1: [tex]\( 2x - 2.1 = 7.5 \)[/tex]
- Plug in [tex]\( x = 2.7 \)[/tex]:
[tex]\[
2(2.7) - 2.1 = 5.4 - 2.1 = 3.3 \quad (\text{not equal to 7.5})
\][/tex]
- Option 2: [tex]\( 4.2 + y = 7.5 \)[/tex]
- Plug in [tex]\( y = 2.1 \)[/tex]:
[tex]\[
4.2 + 2.1 = 6.3 \quad (\text{not equal to 7.5})
\][/tex]
- Option 3: [tex]\( y - 4.2 = 7.5 \)[/tex]
- Plug in [tex]\( y = 2.1 \)[/tex]:
[tex]\[
2.1 - 4.2 = -2.1 \quad (\text{not equal to 7.5})
\][/tex]
From evaluating all these expressions, none match a condition directly relating to determining [tex]\( x \)[/tex]. However, through correct substitution related to the perimeter equation, the value of [tex]\( x \)[/tex] has been found as 2.7 meters. The question is primarily focused on the setup of the equations using given variables and conditions; the provided conditions are used to arrive at establishing [tex]\( x \)[/tex]'s formula.
### Step-by-step Solution
1. Understand the triangle properties:
- An isosceles triangle has two sides that are equal in length. Let’s assume these two equal sides are each [tex]\( x \)[/tex].
- The shortest side is given as [tex]\( y = 2.1 \)[/tex] meters.
2. Formula for Perimeter:
- The formula for the perimeter [tex]\( P \)[/tex] of an isosceles triangle is:
[tex]\[
P = x + x + y = 2x + y
\][/tex]
- Substituting the given perimeter and the shortest side ([tex]\( y = 2.1 \)[/tex]):
[tex]\[
7.5 = 2x + 2.1
\][/tex]
3. Solve the equation for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( 2x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Simplify the equation:
[tex]\[
2x = 5.4
\][/tex]
- Divide by 2 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
4. Check the options:
- Option 1: [tex]\( 2x - 2.1 = 7.5 \)[/tex]
- Plug in [tex]\( x = 2.7 \)[/tex]:
[tex]\[
2(2.7) - 2.1 = 5.4 - 2.1 = 3.3 \quad (\text{not equal to 7.5})
\][/tex]
- Option 2: [tex]\( 4.2 + y = 7.5 \)[/tex]
- Plug in [tex]\( y = 2.1 \)[/tex]:
[tex]\[
4.2 + 2.1 = 6.3 \quad (\text{not equal to 7.5})
\][/tex]
- Option 3: [tex]\( y - 4.2 = 7.5 \)[/tex]
- Plug in [tex]\( y = 2.1 \)[/tex]:
[tex]\[
2.1 - 4.2 = -2.1 \quad (\text{not equal to 7.5})
\][/tex]
From evaluating all these expressions, none match a condition directly relating to determining [tex]\( x \)[/tex]. However, through correct substitution related to the perimeter equation, the value of [tex]\( x \)[/tex] has been found as 2.7 meters. The question is primarily focused on the setup of the equations using given variables and conditions; the provided conditions are used to arrive at establishing [tex]\( x \)[/tex]'s formula.
Thank you for reading the article The isosceles triangle has a perimeter of 7 5 m Which equation can be used to find the value of tex x tex if the. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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