Pythagorean Theorem Practice

Find the length of the segment that joins the points (-5, 4) and (6, -3).

• 13

• 6

Answer explanation

To get the legs of the right triangle, find the difference between the x coordinates and the difference between the y coordinates.

Then use the Pythagoran Theorem to find the hypotenuse.

Tags

CCSS.HSG.GPE.B.7

Select the right triangle, given the lengths of the sides.

• A

• B

• C

Answer explanation

Use the pythagorean theorem to find out which triangle makes a^2 + b^2 = c^2 true.

Remember when you square a square root, they cancel each other and you get the original number.

Tags

CCSS.8.G.B.8

Elena wonders how much water it would take to fill her cup. She drops her pencil in her cup and notices that it just fits diagonally. The pencil is 15 cm long and the cup is 12 cm tall. How much water can the cup hold? Explain or show your reasoning. (The volume of a cylinder is π r^2 h.)

• 108π cubic cm

• about 763 cubic cm

• about 3052 cubic cm

• 972π cubic cm

Answer explanation

Use the Pythagorean Theorem to find the diameter of the glass, then take half of the diameter to find the radius. Use the radius and height to find the volume - how much it can hold.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Elena wonders how much water it would take to fill her cup. She drops her 20 cm pencil in her 16 cm cup and notices that it just fits diagonally. Once she uses the Pythagorean Theorem to find the diameter is 12 cm, how does she find the volume?

• She needs to substitute the 16 cm height and the 12 cm diameter into the volume formula.

• She needs to substitute the 16 cm height and the 6 cm radius into the volume formula.

• She needs to substitute the 20 cm height and the 6 cm radius into the volume formula.

Answer explanation

Use the Pythagorean Theorem to find the diameter of the glass, then take half of the diameter to find the radius. Use the radius and height to find the volume - how much it can hold.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Elena wonders how much water it would take to fill her cup. She drops her 10 inch pencil into her 8 inch cup and notices that it just fits diagonally. How can she use this information to find the volume of the cup?

• She can use the Pythagorean Theorem to find how much the cup will hold

• She can use the Pythagorean Theorem to find the height of the cup

• She can use the Pythagorean Theorem to find the diameter of the cup.

Answer explanation

Use the Pythagorean Theorem to find the diameter of the glass, then take half of the diameter to find the radius. Use the radius and height to find the volume - how much it can hold.

Tags

CCSS.8.G.B.8

Each of the following gives the lengths, in inches, of the sides of a triangle. Which one is a right triangle?

• 3, 4, 6

• 4, 6, 8

• √5, √12, √13

• √5, √5, √10

Tags

CCSS.8.G.B.8

Each of the following gives the lengths, in inches, of the sides of a triangle. Which one is a right triangle?

• 3, 4, 6

• 4, 6, 8

• 5, 12, 13

• 5, 5, 10

Tags

CCSS.8.G.B.8

Clare has a 2-liter bottle full of water. A cone-shaped paper cup has diameter 18 cm and slant height 15 cm as shown. Can she pour all the water into one paper cup? Explain your reasoning. (The volume of a cone is 1/3πr²h and 2 liter = 2,000 cubic centimeters.)

• yes, the volume of the cone is about 5,087 cubic centimeters, which is more than 2,000 cubic cm

• yes, the volume of the cone is about 3,815 cubic centimeters, so it can hold 2,000 cubic cm

• no, the volume of the cone is about 1,272 cubic centimeters, so it can't hold 2,000 cubic cm

Answer explanation

Use the Pythagorean Theorem to find the height of the cone, then find the radius by taking half of the diamter.

Use the radius and height to find the volume.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Solve for x. 

• 38.9
• 40.2
• 45.6
• 54

Tags

CCSS.8.G.B.8

Use the distance formula to find AB to the nearest tenth.

• AB = 5.7

• AB = 4.5

• AB = 4.8

• AB = 5.4

Tags

CCSS.HSG.GPE.B.7