+0  
 
+1
1776
2
avatar+1796 

In $\triangle ABC$, $AB = 5$ cm, $BC = 10$ cm, and the altitude drawn to $\overline{AB}$ is 8 cm. What is the number of centimeters in the length of the altitude to $\overline{BC}$?

 Aug 22, 2015

Best Answer 

 #2
avatar+94611 
+11

According to Melody's diagram, the triangle formed by the origin and B and C has an area of (1/2)*(8)*(6) = 24 sq cm

 

And the triangle formed by the origin and A and C has an area of (1/2)*(1)*(8)  = 4 sq cm

 

So  the area formed by triangle  ABC must be the difference of these = 20 sq cm

 

And this is given by (1/2)(10)h = 20   ....so.....→ 5h = 20   → h = 4 (cm) 

 

This can also be seen by similar triangles.....Call the origin "D"    ....and we have

 

BC /CD = AB/h

 

10/8  = 5/h   → h = (5)(8)/(10)  = 40/10  = 4 (cm)

 

 

 Aug 23, 2015
 #1
avatar+95361 
+10

 Hi Mellie :)

 

$$\\In $\triangle ABC$, $AB = 5$ cm, $BC = 10$ cm, and the altitude drawn to $\overline{AB}$ is 8 cm. $\\$What is the number of centimeters in the length of the altitude to $\overline{BC}$?$$

 

Let h=altitude to BC

When I tried to draw the pic I realized that the altitude to AB had to lie outside the triangle.

That is, angle CAB is an obtuse angle.

 

 

Area of triangle ABC = 1/2 * 5*8 = 20cm^2       (error fixed - thanks Chris) 

Area of triangle also = 1/2 * BC * altitude to BC = 1/2 * 10* h = 5h cm^2

 

so      5h=20

h=4

The altitude to BC is 4 cm

 Aug 23, 2015
 #2
avatar+94611 
+11
Best Answer

According to Melody's diagram, the triangle formed by the origin and B and C has an area of (1/2)*(8)*(6) = 24 sq cm

 

And the triangle formed by the origin and A and C has an area of (1/2)*(1)*(8)  = 4 sq cm

 

So  the area formed by triangle  ABC must be the difference of these = 20 sq cm

 

And this is given by (1/2)(10)h = 20   ....so.....→ 5h = 20   → h = 4 (cm) 

 

This can also be seen by similar triangles.....Call the origin "D"    ....and we have

 

BC /CD = AB/h

 

10/8  = 5/h   → h = (5)(8)/(10)  = 40/10  = 4 (cm)

 

 

CPhill Aug 23, 2015

31 Online Users

avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.