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vekshin1
3 years ago
13

Sofia tem 52 triângulos retângulos isósceles iguais. Ela quer fazer quadrados usando alguns desses triângulos. Ela pode fazer qu

adrados de quantos tamanhos diferentes?
Mathematics
1 answer:
oee [108]3 years ago
8 0

Answer:

Portanto, o Sofia pode fazer 6 tamanhos diferentes

Step-by-step explanation:

A fim de sermos capazes de determinar efetivamente quantos quadrados de diferentes tamanhos podem ser formados a partir do triângulo isósceles 52, resolvemos isso usando a fórmula

2 (n + 1) Onde n = 0 e todos os inteiros positivos

em outro para obter um tamanho diferente para os quadrados, temos que adicionar mais triângulos para aumentar o tamanho

a) quando n = 0

2 (0 + 1) = 2 × 1 = 2 triângulos isósceles iguais

A união de 2 triângulos isósceles forma um quadrado. Este é o primeiro quadrado

= 1 quadrado

b) quando n = 1

2 (1 + 1) = 2 × 2 = 4 triângulos isósceles iguais = 1 quadrado

c) quando n = 2

2 (2 + 1) = 2 × 3 = 6 triângulos isósceles iguais = 1 quadrado

d) quando n = 3

2 (3 + 1) = 2 × 4 = 8 triângulos isósceles iguais = 1 quadrado

e) quando n = 4

2 (4 + 1) = 2 × 5 = 10 triângulos isósceles iguais = 1 quadrado

f) quando n = 5

2 (5 + 1) = 2 × 6 = 12 triângulos isósceles iguais = 1 quadrado

Adicionamos o número total de triângulos usados

2 + 4 + 6 + 8 + 10 + 12 = 42 triângulos

42 triângulos de 52 triângulos formariam 6 quadrados com tamanhos diferentes

Vamos fazer mais um, onde n = 6

g) quando n = 6

2 (6 + 1) = 2 × 7 = 14 triângulos isósceles iguais = 1 quadrado

2 + 4 + 6 + 8 + 10 + 12 + 14 = 56 triângulos

Isso já excedeu o número dado de triângulos em questão.

Portanto, o Sofia pode fazer 6 tamanhos diferentes de quadrados usando 42 triângulos isósceles iguais

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