Question

What is the value of x?

Answer 1

Answer:

The value of x is 7 cm

Step-by-step explanation:

we can see that there are two triangles

smaller triangle and larger triangle

and both triangles are similar

so, the ratio of their sides must be equal

we get

$\frac{5}{5+40}=\frac{3}{3+2x+10}$

now, we can solve for x

$\frac{5}{5+40}=\frac{3}{2x+13}$

we can cross multiply

$5\left(2x+13\right)=\left(5+40\right)\cdot \:3$

$5\left(2x+13\right)=135$

Divide both sides by 5

$\frac{5\left(2x+13\right)}{5}=\frac{135}{5}$

$2x+13=27$

Subtract both sides by 13

$x+13-13=27-13$

$2x=14$

divide both sides by 2

$\frac{2x}{2}=\frac{14}{2}$

$x=7$

Answer 2

Answer:

The value of x is 7 cm.

Step-by-step explanation:

From the given figure, we know that the two corresponding lines are parallel and so the two given triangles are congruent to each other.

Therefore, the corresponding sides of these triangles will also be proportional so we can write it as:

$\frac{5}{5+40} =\frac{3}{2x+10}$

$\frac{5}{45} =\frac{3}{2x+10+3}$

By cross multiplication:

$10x+65=135$

$10x=135-65$

$10x=70$

$x=\frac{70}{10}$

$x=7$

Therefore, the value of x is 7 cm.