The ratio of the corresponding sides of two similar triangles is 3:2. The sides of the larger triangle are 15 cm, 24 cm, and 27 cm. What are the lengths of the sides of the smaller triangle?
15/x = 3/2 therefore 2 times 15 = 3 times x
30 = 3x
10 = x
24/x = 3/2 therefore 2 times 24 = 3 times x
48 = 3x
16 = x
27/x = 3/2 same as above x = 18
the other sides are 10, 16, and 18
To find the lengths of the sides of the smaller triangle, we need to set up a proportion using the ratio of the corresponding sides of the two similar triangles.
Given:
Ratio of corresponding sides of two similar triangles: 3:2
Sides of the larger triangle: 15 cm, 24 cm, and 27 cm
Let's label the sides of the larger triangle as follows:
Side a in the larger triangle = 15 cm
Side b in the larger triangle = 24 cm
Side c in the larger triangle = 27 cm
Now, we can set up the proportion using the corresponding sides of the two triangles:
a/little a = b/little b = c/little c
Plugging in the values:
15/little a = 24/little b = 27/little c
We are given the values for side a, b, and c in the larger triangle, so let's find the corresponding sides in the smaller triangle:
15/little a = 24/little b
Cross-multiplying, we get:
15 * little b = 24 * little a
This simplifies to:
little b = (24 * little a) / 15
Similarly,
15/little a = 27/little c
Cross-multiplying, we get:
15 * little c = 27 * little a
This simplifies to:
little c = (27 * little a) / 15
Now, we have a system of equations:
little b = (24 * little a) / 15
little c = (27 * little a) / 15
Since we have two equations, we can solve for two variables. Let's solve for little b and little c in terms of little a:
little b = (24 * little a) / 15
little c = (27 * little a) / 15
To find the lengths of the sides of the smaller triangle, we need to determine the value of little a. Unfortunately, the given information does not provide the value of little a, so we cannot determine the exact lengths of the sides of the smaller triangle without additional information.
To find the lengths of the sides of the smaller triangle, we can use the concept of ratios in similar triangles.
Given that the ratio of corresponding sides of the two similar triangles is 3:2, we can set up the following proportion:
(Length of a side in the larger triangle) / (Length of the same side in the smaller triangle) = 3/2
Now, let's assign variables to the lengths of the corresponding sides in the smaller triangle. Let's call the lengths of the sides in the smaller triangle x cm, y cm, and z cm.
Using the proportion, we can set up the following equations:
15 cm / x cm = 3/2
24 cm / y cm = 3/2
27 cm / z cm = 3/2
To solve for x, we can cross-multiply and divide:
15 cm * 2 = 3 * x cm
30 cm = 3x cm
x cm = 10 cm
To solve for y, we can cross-multiply and divide:
24 cm * 2 = 3 * y cm
48 cm = 3y cm
y cm = 16 cm
To solve for z, we can cross-multiply and divide:
27 cm * 2 = 3 * z cm
54 cm = 3z cm
z cm = 18 cm
Therefore, the lengths of the sides of the smaller triangle are 10 cm, 16 cm, and 18 cm.