Answer:
w =
![√(73)](https://img.qammunity.org/2021/formulas/mathematics/high-school/697lk5brlov46qi3dx8z5xc8ody52u8lvr.png)
Explanation:
Applying 3 applications of Pythagoras' identity on the 3 right triangles from left to right.
Left right triangle ( finding vertical side v ), then
v² + 7² = 9²
v² + 49 = 81 ( subtract 49 from both sides )
v² = 32 ( take the square root of both sides )
v =
= 4
![√(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/zk4ls2i7rszmygzgqi2kkfexuqtms266jg.png)
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Middle right triangle ( finding hypotenuse h ), then
h² = 5² + v² = 5² + (4
)² = 25 + 32 = 57 ( square root of both sides )
h =
![√(57)](https://img.qammunity.org/2021/formulas/mathematics/high-school/r4g7re5i64ixyqxbt002u149a15hu298q5.png)
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Right side right triangle ( finding hypotenuse w ), then
w² = 4² + h² = 4² + (
)² = 16 + 57 = 73 ( square root of both sides )
w =
![√(73)](https://img.qammunity.org/2021/formulas/mathematics/high-school/697lk5brlov46qi3dx8z5xc8ody52u8lvr.png)