An isosceles trapezoid with a perimeter of 42 inches. each of the congruent non parallel sides is 5 inches long, and the trapezoid is 3 inches tall. how long are the two parallel sides? a. 10 in, 22 in b. 16 in, 16 in c. 10 in, 16 in d. 12 in, 20 in

Longer - 20 in and Shorter - 12 in

Step-by-step explanation:

We know that when we subtract the shorter side from longer we get two cuts named  x:

2 x = a - b  => a - b = 2 x

One of this section ( x ) with height ( h ) and lateral (congruent non parallel) side ( c ) make right triangle, from which we get:

x² = c² - h²  and c = 5 in, h = 3 in

x² = 5² - 3² = 25 - 9 = 16 => x = √16 = 4 => x = 4 in

Now we will replace x = 4  in the equation  a - b = 2 · 4 = 8 and get first equation of the system.

a - b = 8

We also know that the formula for calculating perimeter is:

P = a + b + 2 c  where P = 42 in and c = 5 in

a + b = 42 - 2 · 5 = 42 - 10 = 32

Now  we get the second equation of the system:

a + b = 32

a - b = 8  

When we add first equation to the second we get:

2 a = 40 => a = 40 / 2 = 20 => a = 20 in

When we replace a = 20 in the first equation we get:

20 + b = 32  => b = 32 - 20 = 12 => b = 12 in

God with you!!!