The ratio of perimeters is the same as the ratio of the corresponding sides: 8:9.
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Any corresponding length measures of the similar figures will have the same ratio.
I'll do the first two problems to get you started
Problem 1
1/2 = 3/6
1/3 = 2/6
For the first fraction, I multiplied top and bottom by 3. Note how 3 is the denominator of the second fraction.
For the second fraction, I multiplied top and bottom by 2. Note how 2 is the denominator of the first fraction.
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Problem 2
1/2 = 5/10
3/5 = 6/10
Like with problem 1, I multiplied top and bottom of the first fraction by the value 5 which is the denominator of the second fraction. Likewise, I did the same for the second fraction using the first denominator. The steps are essentially the same, but the numbers are different.
Problem 3 will be handled the same way. I'll let you try it out.
Set up two equations.
s + 12 = l , s + l = 74 (these equations represent the problem)
s + (s + 12) = 74 plug in "l" to the second equation.
2s + 12 = 74 combine like terms.
2s + 12 - 12 = 74 - 12 subtract to isolate the variable
2/2s = 62/2 divide to isolate the variable.
s = 31. This means the smaller number is 31.
31 + 12 = 43. since the larger number is 12 more than the smaller, add 12.
l = 43 the larger number has a value of 43.
small number = 31
larger number = 43
hope this helps! :D
Answer:
x=5
From the dashed lines on the two sides of this triangle, we can see that these two sides are congruent, or equal, to each other.
In geometry, if a triangle has two congruent sides, then we can call it a <em>isosceles triangle</em>.
In an isosceles triangle, the corners opposite the congruent sides are also congruent, meaning, that the angle measures of this triangle are: 88, 9x+1, and 9x+1.
We also know that angles in a triangle add up to 180 degrees.
So, we have: 88+(9x+1)+(9x+1) = 180
Simplifying: 18x + 2 = 92
Solving: 18x = 90, so x=5
Hope this helps!
180 steel rods to be exact
