Question

The diagram shows a 7cm x 6cm rectangle-based pyramid

Answer 1

Answer:

MT = 8.9 cm

Step-by-step explanation:

In the rectangle ABCD, Angle ABC = 90 degree

In the triangle ABC, Angle B = 90 degree

=> ABC is the right angle triangle

According to the Pythagoras theorem, we have the following equation:

+) $AB^{2} + BC^{2} = AC^{2}$

⇔$6^{2} + 7^{2} = AC^{2}$

⇔$AC^{2} = 36 + 49 = 85$

⇔ $AC = \sqrt{85}$ cm

In the rectangle ABCD, M is the midpoint, so that it is also the midpoint of line segment AC.

=> AM = $\frac{AC}{2}=\frac{\sqrt{85} }{2}$ cm

TM is the height of the pyramid, so that it is perpendicular to the base ABCD.

As AM belongs to the surface of the rectangle ABCD

=> TM is also perpendicular to AM

=> AMT is the right-angled triangle with Angle AMT = 90 degree

According the Pythagoras theorem, we have the following equation:

$AM^{2} + MT^{2} = AT^{2}$

⇔ $MT^{2} = AT^{2} - AM^{2} = 10^{2} - (\frac{\sqrt{85} }{2} )^{2}$

⇔$MT^{2} = 100 - \frac{85}{4} = \frac{315}{4}$

⇔$MT = \sqrt{\frac{315}{4} } =\frac{3\sqrt{35} }{2}$ ≈ 8.9 cm

MT = 8.9 cm