Given: ΔTSP, TS = SP = 10cm, TP = 12cm. Find: Three altitudes of ΔTSP.

for this one I only got one of the altitudes

2 √61

can you give me the other two and tell me if this one is right, sorry I am in a rush

So how what would be all 3?

answer is: 9.6,9.6, and 8

If SU┴TP, SU=8 (think 3-4-5 triangle)

Since the area is 1/2 bh using any side as a base, the other two altitudes can be found via

8*12 = 10h

No problem! I'll help you find the remaining two altitudes of triangle ΔTSP. First, let's verify if the altitude you found, 2√61, is correct.

To find the length of an altitude, we need to use the formula:
Area = 0.5 * base * height

Let's calculate the area of triangle ΔTSP using the given information:
Area = 0.5 * SP * TP
= 0.5 * 10cm * 12cm
= 60cm^2

Now, to find the length of the altitude corresponding to the side TS, we can use the formula for the altitude:
Height (TS) = (2 * Area) / base
Height (TS) = (2 * 60cm^2) / 12cm
Height (TS) = 10cm

Therefore, the length of the altitude corresponding to side TS is 10cm, not 2√61.

Now, let's find the remaining two altitudes:

1. Altitude corresponding to side SP:
Height (SP) = (2 * Area) / base
Height (SP) = (2 * 60cm^2) / 10cm
Height (SP) = 12cm

So, the length of the altitude corresponding to side SP is 12cm.

2. Altitude corresponding to side TP:
To find the altitude corresponding to side TP, we can apply the Pythagorean theorem.

Since we know the lengths of TP (12cm) and TS (10cm), we can use the theorem on triangle TSP:

TP^2 = TS^2 + SP^2
12cm^2 = 10cm^2 + SP^2
SP^2 = 144cm^2 - 100cm^2
SP^2 = 44cm^2

Now, to find the length of the altitude corresponding to side TP, we can use the formula:
Height (TP) = (2 * Area) / base
Height (TP) = (2 * 60cm^2) / 12cm
Height (TP) = 10cm

Therefore, the length of the altitude corresponding to side TP is also 10cm.

To summarize, the altitudes of triangle ΔTSP are:
- Height (TS) = 10cm
- Height (SP) = 12cm
- Height (TP) = 10cm