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2 years ago

Two vertices are 3x+10 and x+60 find x

Mathematics

1 answer:

Morgarella [4.7K]2 years ago

7 0

The value of x such that the vertices 3x + 10 and x + 60 are equal is 25

<h3>What are vertices?</h3>

Vertices are the endpoints or corners of a shape (such as triangle, square, rectangle and related shapes)

<h3>How to determine the value of x?</h3>

The two vertices are given as:

3x + 10 and x + 60

The condition on the two vertices are not given.

So, we assume that the vertices are equal (as in the base angles of an isosceles triangle)

So, we have the following equation

3x + 10 = x + 60

Subtract x from both sides of the equation

2x + 10 = 60

Subtract 10 from both sides of the equation

2x = 50

Divide both sides of the equation by 2

x = 50/2

Evaluate the quotient

x = 25

Hence, the value of x such that the vertices 3x + 10 and x + 60 are equal is 25

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$\begin{gathered} a^2+b^2=c^2 \\ (x)^2+(x+1)^2=5^2\text{ (Replacing the values)} \\ x^2+x^2+2x+1=25\text{ (Raising both terms to the power of 2)} \\ x^2+x^2+2x=25-1\text{ (Subtracting 1 from both sides of the equation)} \\ 2x^2+2x=24\text{ (Adding like terms)} \\ 2x^2+2x\text{ }-24=0\text{ (Subtracting 24 from both sides of the equation)} \\ 2(x+4)(x-3)=0\text{ (Factoring)} \\ x1=-4\text{ (Since x=-4 makes the factor (x+4) equal to 0)} \\ x2=3\text{ (Since x=3 makes the factor (x}-3\text{) equal to 0)} \\ \text{ Since we need a positive solution x would be equal to 3} \end{gathered}$

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