Grade 8 · Math

8th grade Right triangles in real life and in boxes worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Right triangles in real life and in boxes

Grade 8 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

Jun measures an old TV screen: 9 inches tall and 12 inches wide. Screens are measured corner to corner. How long is this screen's diagonal, in inches?
Kira's school garden is a rectangle 5 meters by 12 meters, with a straight path from one corner to the opposite corner. How long is the path, in meters?
Luz's classroom rug is a rectangle 6 feet by 8 feet. A sleepy cat stretches across it corner to corner. How far is it from corner to corner, in feet?
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Strip under it: 13 × 13 = ?, 5 × 5 = ?, take the small square off the big one = ?, then ? × ? = that area, the same whole number in both boxes.
Milo helps steady a 13-foot ladder against the shed wall. Its foot is 5 feet from the wall. How high up the wall does the ladder reach, in feet?
A 5-foot rope runs from the top of Noah's tent pole to a peg 3 feet from the pole. How tall is the pole, in feet?
Pia flies a kite on 10 meters of string, standing 6 meters from the spot right under the kite. How high is the kite, in meters?
Ren's old TV screen measures 20 inches corner to corner, and it is 16 inches wide. How tall is the screen, in inches?
On Tala's small sailboat, a 10-foot rope runs from the top of the mast to the deck, 8 feet from the mast. How tall is the mast, in feet?
9.
Ari cuts straight across a rectangular lawn that is 20 meters by 21 meters. The path across is d meters long. Which equation fits the story?
- d² + 20² = 21²
- 20 + 21 = d
- 20² + 21² = d²
10.
Bo's kite string is 41 meters long, and the kite is 40 meters across the field from Bo. The kite's height is h. Which equation fits the story?
- 40 + h = 41
- 40² + 41² = h²
- 40² + h² = 41²

8th grade Right triangles in real life and in boxes worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Right triangles in real life and in boxes. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the right triangle in a story: a ladder on a wall, a kite string, a TV screen, a path across a field.
I can find the missing side, whole or to the nearest tenth, and say which side is the hypotenuse.
I can find how much a shortcut saves, how tall a tent or roof is, and how long a box's diagonal is.

Standard: 8.G.B.7 (real-world, two and three dimensions)

Words to know

right angle: A square corner, like where a wall meets the ground.

hypotenuse: The side across from the right angle; the longest side.

diagonal: A straight line from one corner to the opposite corner.

sketch: A quick drawing of the story's triangle with the right angle marked.

floor diagonal: The line across the bottom of a box, corner to corner.

box diagonal: The line from a bottom corner to the opposite top corner.

Common mistakes

Your child added the lengths of the sides to get the long side. In a right triangle the squares on the short sides add up to the square on the long side; the lengths do not.

Your child found the area of the square on the missing side but gave that area as the length. The length is the number that times itself makes the area.

Your child subtracted one length from another to get a missing short side. The square on the long side minus the square on the known short side gives the missing square. Try a 5-foot rope and a 3-foot gap: 5 − 3 is 2, but the pole is 4 feet.

What to say

Ask: can the shortcut be as long as walking around?

Ask: which number times itself makes it?

Questions parents ask

What is the most common mistake with right triangles in real life and in boxes?

Your child added the lengths of the sides to get the long side. In a right triangle the squares on the short sides add up to the square on the long side; the lengths do not.

How can I help my child with right triangles in real life and in boxes?

Ask: can the shortcut be as long as walking around?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

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