the longest side of a right-angled triangle is 13 cm. if the perimeter of the triangle is 30 cm, find the shortest side

The shortest side = 5

Step-by-step explanation:

Call one  side = a

The middle side = b

the hypotenuse = c

a^2 + b^2 = c^2

a^2 + b^2 = 13^2

a^2 + b^2 = 169

a + b + c = 30

a + b + 13 = 30

a + b = 17

b = 17 - a

a^2 + b^2 = 169

a^2 + (17 -  a)^2 = 169

a^2 + (289 - 34a + a^2) = 169

a^2 + a^2 - 34a + 289 = 169           Subtract 169 from both sides

2a^2 - 34a + 289 - 169 = 0

2a^2 - 34a + 120 = 0                      Divide by 2

a^2 - 17a + 60 = 0

This quadratic is easily factored. You need two numbers that add to - 17 and multiply to 60

(a - 5) * (a - 12) = 0    Both give you positive answers. You only want the shortest side

a - 5 = 0

a = 5                                              Is 5 the shortest side?

a - 12 = 0

a = 12                                           Yes 5 is the shortest side.

The only mapping shown in the figure is not a function because the 3 is mapped to two different numbers, 1 and 2.

The mapping above has 3 ordered pairs: (3, 1), (3, 2), (7, 5)

Since the x-coordinate 3 is used twice, this relation is not a function.