Question

help me 99 points What is the value of x?

Answer 1

Answer:

x = 12

Step-by-step explanation:

Explanation:-

• Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
• In other words, similar triangles are the same shape , but not necessarily the same size.

• Two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar.
• when we will use SSS(side-side-side) if the measures of corresponding sides are known , then their proportionality can be calculated.
• If all three pairs are in proportion,then the triangles are similar.

      In given diagram

     The two  triangles are similar and their corresponding sides are proportional

    $\frac{4 x+12}{15} = \frac{32}{8} = \frac{68}{17}$

now am taking first two terms

   $\frac{4 x+12}{15} = \frac{32}{8}$

   $\frac{4 x+12}{15} = 4$

cross multiplication and simplify

$4 x+12 = 4X15$

subtracting '12' on both sides,we get

4 x +12 -12 = 60 -12

4 x = 48

dividing '4' on both sides , we get

x = 12

Final answer:- x = 12

verification:-

$\frac{4 (12)+12}{15} = \frac{32}{8} = \frac{68}{17}$

4 = 4 = 4

Answer 2

Both triangles are the same. So, we can find the scale factor the smaller triangle is multipled to get the bigger triangle.

68 / 17 = 4

32 / 8 = 4

The scale factor is 4.

Solve for the missing side.

15 * 4 = 60

Now, we can solve for x because now we know what (4x + 12) should equal.

4x + 12 = 60

4x + 12 - 12 = 60 - 12

4x = 48

4x/4 = 48/4

x = 12

Best of Luck!