# Kindly help me for this triangle problem

#### moonnightingale

The problem is attached. It is triangle and its peak is having value 1

the sides are at a and -a. The new point is on a/4. from which i have drawn perpendicular line

i want to know what is the value of that point on y-axis scale.
book says it is 0.733
but how???

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#### ellensius

The problem is attached. It is triangle and its peak is having value 1

the sides are at a and -a. The new point is on a/4. from which i have drawn perpendicular line

i want to know what is the value of that point on y-axis scale.
book says it is 0.733
but how???
Since I would consider this a typical proportional problem, I wonder that too?

If a can be any number, triangle height y can be 0<y<1 ?

#### Prove It

MHF Helper
The problem is attached. It is triangle and its peak is having value 1

the sides are at a and -a. The new point is on a/4. from which i have drawn perpendicular line

i want to know what is the value of that point on y-axis scale.
book says it is 0.733
but how???
The two known points on that line segment are

$$\displaystyle (a, 0)$$ and $$\displaystyle (0, 1)$$.

$$\displaystyle m = \frac{1 - 0}{0 - a}$$

$$\displaystyle = \frac{1}{-a}$$

$$\displaystyle = -\frac{1}{a}$$.

The $$\displaystyle y$$ intercept is $$\displaystyle 1$$, so $$\displaystyle c = 1$$.

Therefore the line segment has equation

$$\displaystyle y = -\frac{1}{a}\,x + 1$$

$$\displaystyle y = 1 - \frac{x}{a}$$.

So if $$\displaystyle x = \frac{a}{4}$$

$$\displaystyle y = 1 - \frac{\frac{a}{4}}{a}$$

$$\displaystyle = 1 - \frac{1}{4}$$

$$\displaystyle = \frac{3}{4}$$.

• ellensius

#### ellensius

one can do that?
isn't that like saying a=y=1 ?

so all you get is a mirror?
y = 1-x ?

I'm asking since I really don't know.

//====edit
aren't you supposed to plug that back to the equation? so that:
3/4 = -(1/a)x + 1

//====edit 2
wow, that was really stupid of me of course 3/4

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