11. Find the red diagonal of the yellow triangle using the Pythagorean Theorem twice; one time to find the diagonal of the blue triangle and then a second time using your answer to find the diagonal of the yellow triangle.
Length = 22 inches
Height = 10 inches
Depth = 8 inches
To find the red diagonal of the yellow triangle, we need to first find the diagonal of the blue triangle.
First, we find the length of the blue triangle using the Pythagorean Theorem:
Blue triangle diagonal = √(height^2 + depth^2)
Blue triangle diagonal = √(10^2 + 8^2)
Blue triangle diagonal = √(100 + 64)
Blue triangle diagonal = √164
Blue triangle diagonal ≈ 12.81 inches
Now, we use the blue triangle diagonal to find the red diagonal of the yellow triangle using the Pythagorean Theorem again:
Yellow triangle diagonal = √(length^2 + blue triangle diagonal^2)
Yellow triangle diagonal = √(22^2 + 12.81^2)
Yellow triangle diagonal = √(484 + 163.96)
Yellow triangle diagonal = √(647.96)
Yellow triangle diagonal ≈ 25.45 inches
Therefore, the red diagonal of the yellow triangle is approximately 25.45 inches.