Let fghb a right triangle with right angle g and an altitude as shown find xyz

Part 1)

Part 2)

Part 3)

Step-by-step explanation:

step 1

Find the value of z

In the smaller right triangle IFG of the figure

Applying the Pythagoras Theorem

step 2

In the right triangle HFG

Applying the Pythagoras Theorem

-----> equation A

step 3

In the right triangle HIG

Applying the Pythagoras Theorem

-----> equation B

step 4

equate equation A and equation B

step 5

Find the value of y

Substitute the value of x in the equation B

we have

linear pair postulates

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk