MA=18см MB=15см AH:BH=5:4 MN=?

To find the length of MN, we first need to find the length of AB. We can use the given ratio of AH:BH to find the lengths of AH and BH.

AH:BH = 5:4

Let x be the common multiplier for AH and BH. Then:

AH = 5x BH = 4x

Since AH + BH = AB, we have:

5x + 4x = AB 9x = AB

Given that AB = MA + MB:

AB = 18 + 15 AB = 33

So, 9x = 33 x = 33 / 9 x = 3.67

Now we can find the lengths of AH and BH:

AH = 5 * 3.67 AH ≈ 18.35

BH = 4 * 3.67 BH ≈ 14.68

Now, we can find the length of MN by using the ratio of AH:BH:

MN = (AH / BH) * MB MN = (18.35 / 14.68) * 15 MN ≈ 18.78

Therefore, the length of MN is approximately 18.78 cm.