Question

A triangle has two sides that are perpendicular. Could the triangle be isosceles, equilateral, or scalene? Explain.

Answer 1

It could only be scalene or isosceles ... an equilateral triangle has all 60 degree angles
Isosceles- 90-45-45 degrees
Scalene- 90-35-55 degrees

Answer 2

When two lines are described to be "perpendicular" it can be derived that the two intersect and form a right angle (90°).

Knowing this, your given triangle is a right-angled triangle. However, this doesn't mean that it can't be any of the following triangles you mentioned.

〜 Isosceles
A right triangle can be an isosceles triangle so long as two of its lengths and angles are equal. This is possible as the sum of any triangle is 180°, and so if one out of three of the triangle's angles were 90° (the right angle formed by the perpendicular lines) it is still possible that the other two angles are 45° (because 45 + 45 + 90 = 180).

〜 Equilateral
A right triangle can not be an equilateral triangle, as traits of an equilateral triangle include having equal lengths and angles. This would not be possible as all angles in any triangle add to 180°, and a right angle is 90°; meaning that if one were to say a right triangle was also an equilateral, they would be saying that the sum of the angles in that triangle were 90° + 90° + 90° which is equal to 270°, clearly greater than 180°, which is impossible for a triangle.

〜 Scalene
A right triangle can also be a scalene triangle. A scalene triangle has no sides or angles that are equal. So long as the other two angles are not 90° and are unequal to each other, and all add up to 180°, the right triangle can indeed be that of a scalene as well.

All in all, it depends on the lengths of triangle and perhaps any angles you may be given. But for a general answer, yes, it is possible that a triangle with two perpendicular sides be an isosceles or scalene, but not an equilateral.

Hope this helped! :)