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3 years ago

What is the value of x if the sides of a equilateral triangle are x+9 , 3x-9 , and 2x

Mathematics

1 answer:

Yakvenalex [24]3 years ago

3 0

Answer:

x=9

Step-by-step explanation:

The triangle is equilateral which means the sides are equal.

x+9 = 2x

Subtract x from each side

x+9-x = 2x-x

9 =x

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$\Large \boxed{\sf \bf \ \ \dfrac{x^2-x-6}{x^2-3x+2} \ \ }$

Step-by-step explanation:

Hello, first of all, we will check if we can factorise the polynomials.

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$\boxed{x^2+2x-15}\\\\\text{The sum of the zeroes is -2=(-5)+(+3) and the product -15=(-5)*(+3), so}\\\\x^2+2x-15=x^2-3x+5x-15=x(x-3)+5(x-3)=(x+5)(x-3)$

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Now, let's compute the product.

$\dfrac{x^2+6x+8}{x^2+3x-10}\cdot \dfrac{x^2+2x-15}{x^2+3x-4}\\\\\\=\dfrac{(x+2)(x+4)}{(x+5)(x-2)}\cdot \dfrac{(x+5)(x-3)}{(x+4)(x-1)}\\\\\\\text{We can simplify}\\\\=\dfrac{(x+2)}{(x-2)}\cdot \dfrac{(x-3)}{(x-1)}\\\\\\=\large \boxed{\dfrac{x^2-x-6}{x^2-3x+2}}$

So the correct answer is the first one.

Thank you.

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