Based on these sets of side lengths, which triangles are right triangles?

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

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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