Given: ΔBUG ~ ΔBAN, BU = 8 in , UA = 4 in and AN = 24 in. Find the length of GU.
UA? That is not a side in either triangle.
Just recall that corresponding sides have the same ratio.
BU/BA = UG/AN = BG/BN
So plug in the numbers you know.
First, we need to determine the scale factor between the two similar triangles.
Since the triangles ΔBUG and ΔBAN are similar, their corresponding sides are proportional.
We are given that ΔBUG ~ ΔBAN, which means that the ratio of the corresponding sides is the same for both triangles.
We can set up the proportion:
BU / BA = BG / BN
Substituting the given values:
8 / (8 + 24) = BG / 24
Simplifying:
8 / 32 = BG / 24
Next, we cross multiply:
8 * 24 = 32 * BG
192 = 32 * BG
To find BG, we divide both sides of the equation by 32:
BG = 192 / 32
BG = 6 in
Therefore, the length of GU is also 6 inches since BU and BG are the same length.
To find the length of GU, we need to use the information given and the fact that the two triangles ΔBUG and ΔBAN are similar.
The given information tells us that ΔBUG is similar to ΔBAN. This means that the corresponding sides of the two triangles are proportional.
Let's represent the length of GU, which we want to find, as x.
Now, look at the corresponding sides of the two triangles:
BU/BA = GU/AN
Substitute the known values:
8/24 = x/24
Cross-multiply:
8 * 24 = 24 * x
192 = 24x
To solve for x, divide both sides by 24:
x = 192/24
Simplifying, we get:
x = 8
Therefore, the length of GU is 8 inches.