Question

the altitude of a triangle are 12 15 and 20 units the largest angle in the triangle is​

Answer 1

The altitude of a triangle are 12 15 and 20 units the largest angle in the triangle is​ 90°

Step-by-step explanation:

Let the sides of the triangle be a, b and c

Then the area of triangle

$A=\frac{1}{2}\times\text{Base}\times\text{Altitude}$

Thus,

$A=\frac{1}{2}\times a\times 12$

$\implies A=6a$

Similarly

$A=\frac{1}{2}\times b\times 15$

$\implies A=\frac{15b}{2}$

And

$A=\frac{1}{2}\times c\times 20$

$\implies A=10c$

Therefore,

$6a=\frac{15b}{2}=10x$

$\implies 12a=15b=20c$

$\implies \frac{a}{5}=\frac{b}{4}=\frac{c}{3}$   (Dividing by LCM of 12, 15 and 20 i.e. 60)

If the proportionality constant is k then

$a=5k$

$b=4k$

$c=3k$

Now,

$b^2+c^2=(4k)^2+(3k)^2=16k^2+9k^2=25k^2=(5k)^2=a^2$

Therefore, the traingle is a right angled triangle

Therefore, the greatest angle of the triangle will be $90^\circ$

Hope this answer is helpful.

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