Question

Determine o valor de X em cada figura ​

Answer 1

Teorema de Pitágoras:

❑ Fórmula;

$\boxed{\boxed{a {}^{2} = {b}^{2} + {c}^{2} }}$

A)

${x}^{2} = {4}^{2} + 3 {}^{2} \\ x ^{2} = 16 + 9 \\ {x}^{2} = 25 \\\boxed{\boxed{\boxed{\pink{x = 5}}}}$

B)

${y}^{2} = {6}^{2} + 4 {}^{2} \\ {y}^{2} = 36 + 16 \\ {y}^{2} = 52 \\ \boxed{\boxed{\boxed{\pink{y= 2 \sqrt{13} }}}} \\ \\ \\ z {}^{2} = (2 \sqrt{13} ) {}^{2} + 3 {}^{2} \\ z {}^{2} = 52 + 9 \\ z {}^{2} = 61 \\ \boxed{\boxed{\boxed{\pink{z = \sqrt{61} }}}} \\ \\ {x}^{2} = (2 \sqrt{5} ) {}^{2} + ( \sqrt{61} ) {}^{2} \\ {x}^{2} = 20 + 61 \\ {x}^{2} = 81 \\ x = \sqrt{81} \\ \\ \boxed{\boxed{\boxed{\green{x = 9}}}}$

C)

$h {}^{2} = 12 \times 4 \\ h {}^{2} = 48 \\ \boxed{\boxed{h = 4 \sqrt{3} }} \\ \\ {x}^{2} = 4 {}^{2} + (4 \sqrt{3} ) {}^{2} \\ {x}^{2} = 16 + 48 \\ x {}^{2} = 64 \\ x = 8$

D)

$(x + 2) {}^{2} = 6 {}^{2} + x {}^{2} \\ {x}^{2} + 4x + 4 = 36 + {x}^{2} \\ 4x + 4 = 36 \\ 4x = 32 \\ \boxed{\boxed{\boxed{\green{x = 8}}}} \\ \\ \boxed{\boxed{x + 2 = 10}}$

 ✿ ~Sah