Question

Y

4
Solve for y.
Then, find the side lengths of the
largest triangle.
Fill in the green blank.
8
X
2
+
2
8
y
y
[?]
X
Enter
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Answer 1

y = 4
`√(5)` , ? = 10

Explanation:

using Pythagoras' identity on the smallest right triangle

x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )

x =
`√(20)` =
`√(4(5))` =
`√(4)` ×
`√(5)` = 2
`√(5)`

using Pythagoras' identity on the middle right triangle

y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )

y =
`√(80)` =
`√(16(5))` =
`√(16)` ×
`√(5)` = 4
`√(5)`

using Pythagoras' identity on the largest right triangle

?² = x² + y² = (2
`√(5)` )² + (4
`√(5)` )² = 20 + 80 = 100

Take square root of both sides

? =
`√(100)` = 10