Question

find the value of x.
42
6x - 1
10x + 5
78
x = ?

Explanation:

Step1: Apply similar - triangles property

Since the two triangles are similar, the ratios of corresponding sides are equal. So, $\frac{42}{78}=\frac{6x - 1}{10x + 5}$.

Step2: Cross - multiply

$42(10x + 5)=78(6x - 1)$.

Step3: Expand both sides

$420x+210 = 468x-78$.

Step4: Rearrange terms

$468x - 420x=210 + 78$.

Step5: Simplify

$48x=288$.

Step6: Solve for x

$x = 6$.

Answer:

$6$