In the right ∆ABC, the hypotenuse AB = 17 cm. M is the midpoint of the hypotenuse. Find the legs if PAMC=32 cm and PBMC=25 cm

The length of the legs is 8.64cm and 14.64cm respectively

Step-by-step explanation:

I've added an attachment to aid my explanation.

At different intervals, I'll be making reference to it.

Given

From the attachment, we have:

Since, M is the Midpoint

Substitute 17 for AB

Also, from the attachment

Substitute 8.5 for y

--------- (1)

Also, from the attachment

Substitute 8.5 for z

----------- (2)

Subtract (2) from (1)

Make x the subject

Apply Pythagoras Theorem:

We have that:

The above can be replaced with

(see attachment)

Substitute 6 + w for x

Reorder

Solve using quadratic equation:

Where

Split:

or

or

or

But length can't be negative

So:

Recall that:

Hence, the length of the legs is 8.64cm and 14.64cm respectively

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