Corresponding sides of 2 triangles are 6 & 15; if the perimeter of the smaller triangle is 22, what is the perimeter of the larger triangle?
Ratio of sides is 6:15 = 6/15 = 2/5
Ratio of perimeter is 22:x
2:5 = 22:x
2/5 = 22/x
cross multiply and solve for x
misty drew a triangle.one angle is 120 degres.two of the sides measure 5 cm and 8 cm in lengh. the sum of the lengths off all tree sides is 21 cm. wat kind of triangle did misty draw?
Well, it seems like those triangles are quite the odd couple. Let's see if we can solve this riddle together!
If the perimeter of the smaller triangle is 22, we know that the sum of its three sides is 22. Since two corresponding sides are given as 6 and 15, we can assume that the missing side of the smaller triangle is 1.
Now, to find the perimeter of the larger triangle, we need to find the ratio between the corresponding sides. In this case, if the small triangle has a side length of 1 and a corresponding side length of 6, the ratio between them is 1:6.
So, if we multiply the corresponding sides of the larger triangle by the same ratio, we get 6 multiplied by 6 (the ratio). This equals 36.
Therefore, the perimeter of the larger triangle would be 36 + 15 + 6 = 57.
So my dear friend, the perimeter of the larger triangle is 57.
To find the perimeter of the larger triangle, we need to determine the ratio between the corresponding sides of the two triangles.
Let's assume the corresponding sides of the smaller triangle are a and b, and the corresponding sides of the larger triangle are A and B.
According to the given information, a = 6, b = 15, and the perimeter of the smaller triangle is 22.
To find the ratio between the corresponding sides, we can use the formula:
Ratio = (corresponding side of larger triangle) / (corresponding side of smaller triangle)
Using the ratio, we can find the value of A and B.
Ratio = A / a = B / b
A / 6 = B / 15
Now, to find the perimeter of the larger triangle, we add the values of the corresponding sides:
Perimeter of larger triangle = A + B
Now, let's find the value of A:
A / 6 = B / 15
Cross multiplying:
15A = 6B
A = (6B) / 15
Now substitute the value of A in terms of B to find the perimeter of the larger triangle:
Perimeter of larger triangle = (6B) / 15 + B
To simplify this expression, we can find a common denominator:
Perimeter of larger triangle = (6B + 15B) / 15
Perimeter of larger triangle = (21B) / 15
Therefore, the perimeter of the larger triangle is 21B / 15.
To find the perimeter of the larger triangle, we can use the concept of proportional sides in similar triangles.
Similar triangles have corresponding angles that are equal and corresponding sides that are proportional.
In this case, we have two triangles with corresponding sides of 6 and 15, which means they are similar triangles. Let's call the corresponding sides of the larger triangle "x" and "y".
We know that the perimeter of the smaller triangle is 22. The perimeter of a triangle is the sum of its three sides. So, in the smaller triangle, the sum of the three sides is 22:
6 + 6 + 15 = 22
Now, we can set up a proportion using the corresponding sides:
6/x = 22/15
To solve for x, we can cross-multiply and find:
15 * 6 = 22 * x
90 = 22x
Now we can solve for x by dividing both sides of the equation by 22:
x = 90/22
Simplifying this fraction, we get:
x ≈ 4.09
So, the length of the corresponding side in the larger triangle is approximately 4.09.
To find the perimeter of the larger triangle, we need to sum all of its three sides:
x + x + y = 4.09 + 4.09 + 15
Adding these values, we get:
Perimeter of the larger triangle ≈ 23.18
Therefore, the perimeter of the larger triangle is approximately 23.18.