Question

Hello, happy Friday, I am just here with some geometry questions.

Answer 1

Answer:

4

Step-by-step explanation:

The first thing you should notice is that the triangles (the smaller one and the larger one) are similar due to angle-angle similarity (the top angle equals itself, and because the bases are parallel lines cut by a transversal, the base angle of the bigger triangle is equal to the corresponding base of the smaller triangle.

Similar triangles' corresponding sides have equal ratios to one another. That means we can set up an equation: side of smaller triangle ÷ corresponding side of larger triangle = other side of smaller triangle ÷ corresponding side of larger triangle. We plug the values given to us and can change this equation to:$\frac{x}{x + 12} = \frac{x + 1}{x + 16}$ **

We now multiply both sides of the above equation by $(x + 12)(x + 16)$ to get: $x(x + 16) = (x + 1)(x + 12)$

$x^{2} + 16x = x^{2} + 13x + 12$

$3x = 12$

$x = 4$

That means our answer, for the value of x, is 4

** Make sure you don't say $\frac{x}{12} = \frac{x + 1}{15}$, because those aren't the sides of the larger square.

Answer 2

Answer:

$x=4$

Step-by-step explanation:

By the Triangle Proportionality Theorem:

$\displaystyle \frac{x}{12}=\frac{x+1}{15}$

By cross-multiplication:

$\displaystyle 12(x+1)=15(x)$

Distribute:

$12x+12=15x$

Subtract 12x from both sides:

$12=3x$

Hence:

$x=4$