Question

An altitude h of a triangle is increased by a length m.How much must be taken from the corresponding base b so that the area of the new triangle is half of the original triangle?

Answer 1

@maheshmeghwal9 What's the formula for area of a triangle in terms of height and base?

Answer 2

1/2xbasexheight

Answer 3

You have to solve for n
\[
\frac{b h}{4}=\frac{1}{2}
(b-n) (h+m)
\]

Answer 4

Good:)
Let the original triangle's height be h and base b
It's given that height is increased by length l, so new height is \((h+l)\)
Now we want the new triangle's area to be half of the original so we'll have to decrease the base. Let's say we decrease it by x, now base is \((b-x)\)
So this triangle's area is
\[\frac{1}{2}(h+l)(b-x)\]
Relating it to the oriinal triangle's area
\[\frac{1}{2}(h+l)(b-x)=\frac{1}{2}(\frac{1}{2}hb)\]
Can you find x now?

Answer 5

sorry it should be m in place of \(l\)

Answer 6

Ya,Thanx a lot!I got it.

Answer 7

You should find
\[
n=\frac{b (h+2 m)}{2 (h+m)}
\]