The height of a triangle is 2 cm more than the base. If the height is increased by 2 cm while the base remains the same, the new area becomes 82.5 cm ².

Question

Find the base and the height of the original triangle.

 

a. base = 13 cm; height = 15 cm

b. base =9 cm; height = 11 cm

c. base = 11 cm; height = 13 cm

d. base = 11 cm; height = 15 cm

Answer 1

OK. Remember that a triangle's area is bh/2, where

b = base

h = height

 

So. You start with a triangle of base b and height h, add 2 to the height, and get a triangle of area 82.5.

 

b(h+2)/2 = 82.5

b(h+2) = 165

 

What you want to do from here is test the b and h from the choices given, and figure out which b and h satisfy this.

 

(a) If b=13 and h=15, b(h+2) = 221 nope.

(b) If b=9 and h=11, b(h+2) = 117 nope.

(c) If b=11 and h=13, b(h+2) = 165 that's it!

No need to worry about (d).

 

Another way to look at it: 165 is a multiple of 5. None of your choices for b is a multiple of 5. So to end up with 165, h+2 must as a minimum be a multiple of 5. Choice (c) is the only one that does that. If more than one of the choices did that, then you would have to solve those choices all the way.

 

Cheers!