Question

Solve for x. Round to the nearest tenth

Answer 1

Answer:

x =23.9 (which matches the last option in the list of possible answers)

Step-by-step explanation:

Notice that we can use ratios among sides of similar triangles to solve this problem. Notice the two triangles in question. The small triangle is that with sides (x-1) and 20, while the larger triangle is that of larger sides built by the addition of (x-1) + 8 , and by 20 + 7

So we can relate similar sides with their ratios, and say that side (x-1)+8 is to side (x-1) the same as side (20 +7) is to side 20. Such put in math terms becomes the following proportion:

$\frac{(x-1)+8}{(x-1)} =\frac{20+7}{20} \\\frac{(x+7}{(x-1)} =\frac{27}{20}$

we can now solve for the unknown "x" in the rational equation above, by cross multiplication:

$\frac{(x+7)}{(x-1)} =\frac{27}{20}\\20\,*\,(x+7)= 27\,*\,(x-1)\\20x+140=27x-27\\140+27=27x-20x\\167=7x\\x=\frac{167}{7} \\x=23.8571$

which we can round to 23.9 to match the last option in the list of possible answers.