Question

For the given side lengths of a triangle, match the following to the type of triangle.

• A. Isosceles Right △
• B. Isosceles △
• C. Scalene Right △
• D. Scalene △

Answer 1

Let's take the sides one by one and try to find the type of triangle.
A. $3,4,5$
The sides are not equal, hence it's a scalene triangle.
Moreover, $3^2+4^2=25=5^2$
$\therefore$ It's a right triangle too,
Hence, it's a scalene right triangle.
B. $2,3,4$
The sides are not equal, hence it's a scalene triangle.
Moreover, $2^2+3^2=13\ne 4^2$
$\therefore$ It's not a right triangle.
Hence, it's a scalene triangle.
C. $4,4,5$
Two sides are equal, hence it's an isoceles triangle.
Moreover, $4^2+4^2=32\ne 5^2$
$\therefore$ It's not a right triangle,
Hence, it's an isosceles triangle.
D. $3,3,3\sqrt{2}$
Two sides are equal, hence it's an isosceles triangle.
Moreover, $3^2+3^2=18=(3\sqrt{2}{)}^2$
$\therefore$ It's a right triangle too,
Hence, it's an isosceles right triangle.