Question

What kind of a triangle is formed by the points (3, 0), (7, 0), (8, 3) ?

• A. Scalene
• B. Isosceles
• C. Equilateral
• D. Right triangle

Answer 1

The correct option is A Scalene

Let A, B and C represents the points
(3, 0), (7, 0) and (8, 3) respectively.

$AB=\sqrt{(3-7{)}^2+(0-0{)}^2}$

$=\sqrt{(-4{)}^2+0}=\sqrt{16}=\sqrt{4^2}$

AB = 4 units

$BC=\sqrt{(7-8{)}^2+(0-3{)}^2}$

$=\sqrt{(-1{)}^2+(-3{)}^2}$

$=\sqrt{1+9}=\sqrt{10}$

$\therefore BC=\sqrt{10}units$

$AC=\sqrt{(3-8{)}^2+(0-3{)}^2}$

$=\sqrt{(-5{)}^2+(-3{)}^2}$

$=\sqrt{25+9}=\sqrt{34}$

$\therefore AC=\sqrt{34}units$

$\because AB=4,BC=\sqrt{10},AC=\sqrt{34}$

$AB\ne BC\ne AC$

Now, let's apply Pythagoras theorem to see if the triangle is a right triangle.

As, AC is the longest, we have,

$A{B}^2+B{C}^2=(4{)}^2+(\sqrt{10}{)}^2=16+10$

$=26\ne 34$

$\therefore A{B}^2+B{C}^2\ne A{C}^2$

Thus, given points form a SCALENE triangle.

Hence, option a is correct.