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The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of [tex]x[/tex] if its shortest side, [tex]y[/tex], measures 2.1 m?

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]

Answer :

We are given an isosceles triangle with a perimeter of [tex]$7.5\,\text{m}$[/tex]. One of its sides (presumably the base) measures [tex]$2.1\,\text{m}$[/tex], and the two equal sides each have a length of [tex]$x$[/tex]. The perimeter of a triangle is the sum of the lengths of its sides. Therefore, we can set up the following equation:

[tex]$$
2.1 + x + x = 7.5
$$[/tex]

Combining like terms gives:

[tex]$$
2.1 + 2x = 7.5
$$[/tex]

This is the equation used to find the value of [tex]$x$[/tex].

To solve for [tex]$x$[/tex], we subtract [tex]$2.1$[/tex] from both sides:

[tex]$$
2x = 7.5 - 2.1 = 5.4
$$[/tex]

Then, we divide both sides by [tex]$2$[/tex]:

[tex]$$
x = \frac{5.4}{2} = 2.7
$$[/tex]

Thus, the equation used is:

[tex]$$
2.1 + 2x = 7.5
$$[/tex]

and we find that [tex]$x=2.7\,\text{m}$[/tex].

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Rewritten by : Jeany

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