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Karolina [17]
3 years ago
12

Use the following image to assist in your answer. a = - 6 - 9 - 4

Mathematics
1 answer:
vfiekz [6]3 years ago
8 0

Step-by-step explanation:

Pythagoras' theorem for the smallest one :

c^2 = 4^2 + 6^2

c^2 = 16 + 36

c^{2} = 52

Pythagoras' theorem for the middle one :

b^{2} = 6^{2} + a^{2}

Pythagoras' theorem for the biggest one :

(4+a)^2 = c^2 + b^2

16 + 8a + a^2 = 52 + b^2

Using the formula before (for b^2) it becomes :

16 + 8a + a^2 = 52 + (6^2 + a^2)

16 + 8a + a^2 = 52 + 6^2 + a^2

16 + 8a = 52 + 6^2

16 + 8a = 52 + 36

16+8a = 88

8a = 88-16

8a = 72

a = \frac{72}{8}

a = 9

Verifying :

b^2 = 6^2 + a^2

b^2 = 36 + 81

b^2 = 117

b^{2} = 117

The biggest one :

(4+a)^2 = c^2 + b^2

(4+9)^2 = 52 + 117

13^2 = 169

True

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