Question

WILL MARK BRAINLIEST IF
- Answer is correct


- Answer is detailed



WILL NOT MARK BRAINLIEST IF:


-Answer contains links


-Answer not detailed


-Answer incorrect



(P.s: must be 2 answers pls)

Thanks

Answer 1

Hi there!

We can begin by calculating the segment AC using the Pythagorean theorem.

$AC^2 = AB^2 + BC^2$

Plug in the given values:

$AC^2 = 6^2 + 7^2\\\\AC^2 = 85\\\\AC = 9.22 cm$

Now, we can construct a new triangle using AM, MT, and AT.

Since "M" is the midpoint of AC:

AC = 2AM

9.22 = 2AM

AM = 4.61 cm

AT is the hypotenuse in this instance and AM is one of the legs, so:

$AT^2 = AM^2 + MT^2\\\\10^2 = 4.61^2 + MT^2\\\\78.75 = MT^2\\\\MT = 8.87 \approx \boxed{8.9 cm}}$

Answer 2

Answer:

8.9 cm

Step-by-step explanation:

First, we'll work out the length of AC

By Pythagoras,

$AC=\sqrt{6^2+7^2}\\=\sqrt{36+49}\\=\sqrt{85}$

Half of this is the length of MC, $\frac{\sqrt{85}}{2}$.

Now consider the triangle TMC, which is also a right triangle.

By Pythagoras,

$MT=\sqrt{10^2-(\frac{\sqrt{85}}{2})^2}\\\\=\sqrt{100-\frac{85}{4}}\\=\sqrt{\frac{315}{4}}$

Which is 8.9 cm to 1 d.p.