Answer:
7) 28.8 in
8) 80.6 mm
9) 68.3 cm
(All answers to the nearest tenth)
Explanation:
7) The traingle is a right-angled triangle since the 4 angles of a rectangle are right angles.
Applying Pythagoras' Theorem,
x²= 16² +24²
x²= 832
x= √832
x= 28.8 in (nearest tenth)
8) Applying Pythagoras' Theorem,
x² +40²= 90²
x²= 8100 -1600
x²= 6500
x= 80.6 mm (nearest tenth)
9) See the attached picture for better understanding.
1st picture shows the simplified diagram of the question, indicating where line x lies in the rectangular prism.
Now, if we cut the prism into half diagonally so that we obtain 2 equal triangular prism, we would obtain 2 prisms that look like the one drawn in picture 2.
Now zoom in to the blue face of the prism, we would get a triangle as shown in picture 3.
Let's find the value of y.
Applying Pythagoras' Theorem,
y²= 40² +54²
y²= 4516
y= √4516
Look at picture 2 again at focus at the pink shaded triangle. It has been re-drawn in picture 4.
Now we know that y= √4516.
Applying Pythagoras' Theorem,
x²= (√4515)² +12²
x²= 4660
x= √4660
x= 68.3 cm (nearest tenth)