Answer:
8 units, 3 units, √73 units
16 units, 30 units, √50 units
Step-by-step explanation:
Given the above side lengths of a triangle, to determine which triangles are right triangles, we would make use of the Pythagorean theorem which holds that the sum of the square of two smaller legs of a right triangle would give us the square of the length of the longest leg.
That is a² + b² = c²
Thus, let's check each options given.
Let c be the 3rd units given in each option, which is the longest leg.
Option 1:
c² = 8² + 15²
c² = 64 + 225 = 289
c = √289 = 17
∆ with lengths 8 units, 15 units, √75 units is not a right triangle because c ≠ √75, from calculation.
Option 2:
c² = 8² + 3²
c² = 64 + 9 = 73
c = √73 units
∆ with lengths 8 units, 3 units, √73 units is a right triangle because c = √73 from calculation
Option 3:
c² = 16² + 30²
c² = 256 + 900 = 1156
c = √1156 = 34
∆ with lengths 16 units, 30 units, √50 units is not a right triangle because c ≠ √50 units from calculation.
Option 4:
c² = 5² + 7²
c² = 25 + 49 = 74
c = √74 units
∆ with lengths 16 units, 30 units, √50 units is a right triangle because c = √74 units from calculation.
Therefore, based on the sets of side lengths given, the following are right triangles:
8 units, 3 units, √73 units
16 units, 30 units, √50 units