Question

Does anyone know this

Answer 1

The value of x is 20.

Solution:

Sides of one triangle are 2x – 4 and 39.

Sides of another triangle are x + 6 and 24.

Property of similar triangle:

If two triangles are similar then their corresponding angles are congruent and the corresponding sides are in the same ratio.

$\frac{2x-4}{24} =\frac{39}{x+6}$

Do cross multiplication.

$(2x-4)(x+6)=39\times 24$

$2x^2+12x-4x-24=936$

$2x^2+8x-24-936=0$

$2x^2+8x-960=0$

Divide by 2 on each of the term.

$x^2+4x-480=0$

Solve using quadratic equation.

$(x-20)(x+24)=0$

$(x-20)=0, \ (x+24)=0$

$x = 20, \ x = -24$

Ignore the negative term, because if you substitute this you will get a negative terms only. But length of sides cannot be in negative measures.

Therefore x = 20.