Answer:
Longer - 20 in and Shorter - 12 in
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!!!