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The isosceles triangle has a perimeter of [tex]$7.5 \, \text{m}$[/tex].

Which equation can be used to find the value of [tex]$x$[/tex] if the shortest side, [tex][tex]$y$[/tex][/tex], measures [tex]$2.1 \, \text{m}$[/tex]?

A. [tex]2x - 2.1 = 7.5[/tex]
B. [tex]4.2 + y = 7.5[/tex]
C. [tex]y - 4.2 = 7.5[/tex]
D. [tex]2.1 + 2x = 7.5[/tex]

Sagot :

GinnyAnswer
Let us determine which equation can be used to find the value of [tex]\( x \)[/tex] in the given isosceles triangle scenario.

Given:
1. The perimeter of the isosceles triangle is [tex]\( 7.5 \)[/tex] meters.
2. The shortest side [tex]\( y \)[/tex] measures [tex]\( 2.1 \)[/tex] meters.

In an isosceles triangle, two sides are equal. Let [tex]\( x \)[/tex] be the length of each of the two equal sides. Thus, the sides can be represented as [tex]\( x \)[/tex], [tex]\( x \)[/tex], and [tex]\( 2.1 \)[/tex].

The formula for the perimeter of a triangle is the sum of all its sides:
[tex]\[ x + x + 2.1 = 7.5 \][/tex]

Simplifying this, we get:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]

Now that we have a simplified equation, we can see that the equation which can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]

So, the correct equation from the given options is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
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