Question

What is the value of x? answer both please. will mark brainliest.

Answer 1

x = 27, x = 3

Solution:

Figure (1):

If two triangles are similar, then the angles are congruent and the corresponding sides are proportional.

$\Rightarrow\frac{x+8}{2x-5} =\frac{10}{14}$

Do cross multiplication.

$\Rightarrow14(x+8)=10(2x-5)$

$\Rightarrow14x+112=20x-50$

Subtract 112 from both side of the equation.

$\Rightarrow14x+112-112=20x-50-112$

$\Rightarrow14x=20x-162$

Subtract 20x from both side of the equation.

$\Rightarrow14x-20x=20x-162-20x$

$\Rightarrow-6x=-162$

Divide by –6 on both sides.

⇒ x = 27

Figure (2):

If two triangles are similar, then the angles are congruent and the corresponding sides are proportional.

$\Rightarrow\frac{3}{4} =\frac{2.25}{x}$

$\Rightarrow3x=4\times2.25$

$\Rightarrow3x=9$

Divide by 3 on both sides of the equation.

$\Rightarrow\frac{3x}{3} =\frac{9}{3}$

⇒ x = 3