Question

Please help me tell me how to do this in simpler steps!!

Answer 1

The perimeters of the right triangles are: Case 1: s = 48 cm, Case 2: s = 24 cm, Case 3: s = 30 cm, Case 4: s = 40 cm. And the length of leg EF is 4.1 cm.

How to determine perimeter and missing lengths in right triangles

In this problem we need to determine the perimeter of four triangles and the missing length of the leg of another right triangle. The procedure for the determination of the perimeter is shown as follows:

1. Determine the length of missing side by Pythagorean theorem.
2. Add the lengths of the three sides.

Now we proceed to determine the perimeters of the right triangles:

Case 1:

`a = √((16 cm)^2+(12 cm)^2)`

a = 20 cm

s = 16 cm + 12 cm + 20 cm

s = 48 cm

Case 2:

`b = √((10 cm)^2-(6 cm)^2)`

b = 8 cm

s = 6 cm + 10 cm + 8 cm

s = 24 cm

Case 3:

`c = √((13 cm)^2 - (12 cm)^2)`

c = 5 cm

s = 13 cm + 12 cm + 5 cm

s = 30 cm

Case 4:

`d = √((8 cm)^2 + (15 cm)^2)`

d = 17 cm

s = 8 cm + 15 cm + 17 cm

s = 40 cm

And the missing side of the right triangle is:

`EF = √((8.9 cm)^2-(7.9 cm)^2)`

EF = 4.1 cm