Question
A triangle has sides of lengths 4.2, 5.7, and 6.2 inches. The smallest side of a similar triangle is 1.4 inches. What are the lengths of the other two sides
Answers
Answered by
GPT 3.5
If the smallest side of the similar triangle is 1.4 inches, and the sides of the original triangle are 4.2, 5.7, and 6.2 inches, then the ratio of the corresponding sides of the similar triangle to the original triangle is 1.4/4.2 = 0.3333...
Let x be the length of the second side of the similar triangle.
Then the length of the second side of the original triangle is 0.3333... * x.
Since the lengths of the sides of the original triangle are 4.2, 5.7, and 6.2 inches, we have the equation:
0.3333... * x = 5.7
To solve for x, we divide both sides of the equation by 0.3333...:
x = 5.7 / 0.3333...
Using a calculator, we find that 5.7 / 0.3333... = 17.1
So, the length of the second side of the similar triangle is 17.1 inches.
Finally, using the same logic, we can find the length of the third side of the similar triangle:
Let y be the length of the third side of the similar triangle.
Then the length of the third side of the original triangle is 0.3333... * y.
Since the lengths of the sides of the original triangle are 4.2, 5.7, and 6.2 inches, we have the equation:
0.3333... * y = 6.2
To solve for y, we divide both sides of the equation by 0.3333...:
y = 6.2 / 0.3333...
Using a calculator, we find that 6.2 / 0.3333... = 18.6
So, the length of the third side of the similar triangle is 18.6 inches.
Let x be the length of the second side of the similar triangle.
Then the length of the second side of the original triangle is 0.3333... * x.
Since the lengths of the sides of the original triangle are 4.2, 5.7, and 6.2 inches, we have the equation:
0.3333... * x = 5.7
To solve for x, we divide both sides of the equation by 0.3333...:
x = 5.7 / 0.3333...
Using a calculator, we find that 5.7 / 0.3333... = 17.1
So, the length of the second side of the similar triangle is 17.1 inches.
Finally, using the same logic, we can find the length of the third side of the similar triangle:
Let y be the length of the third side of the similar triangle.
Then the length of the third side of the original triangle is 0.3333... * y.
Since the lengths of the sides of the original triangle are 4.2, 5.7, and 6.2 inches, we have the equation:
0.3333... * y = 6.2
To solve for y, we divide both sides of the equation by 0.3333...:
y = 6.2 / 0.3333...
Using a calculator, we find that 6.2 / 0.3333... = 18.6
So, the length of the third side of the similar triangle is 18.6 inches.