Triangle inequality. Game on.

Triangle inequality is a grade 7 math skill aligned to Common Core standard 7.G.A.2. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 triangle inequality problems our math games drill.

CCSS 7.G.A.210 questions in the bank
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Warm-upeasy

A triangle has sides of length 44 and 11.11\textsf{.} Which inequality represents the possible lengths, x,x\textsf{,} of the remaining side?

The triangle inequality requires ∣11−4∣<x<11+4.|11 - 4| < x < 11 + 4\textsf{.} Simplifying gives 7<x<15.7 < x < 15\textsf{.}

Mid-gameeasy

A triangle has side lengths 77 and 3.3\textsf{.} Which inequality represents the possible lengths, x,x\textsf{,} of the third side?

The triangle inequality requires ∣7−3∣<x<7+3.|7 - 3| < x < 7 + 3\textsf{.} Simplifying gives 4<x<10.4 < x < 10\textsf{.}

Mid-gameeasy

Two sides of a triangle measure 1313 and 6.6\textsf{.} Which inequality gives the possible lengths, x,x\textsf{,} of the third side?

The triangle inequality requires ∣13−6∣<x<13+6.|13 - 6| < x < 13 + 6\textsf{.} Simplifying gives 7<x<19.7 < x < 19\textsf{.}

Mid-gameeasy

A triangle has side lengths 1414 and 5.5\textsf{.} Which inequality represents the possible lengths, x,x\textsf{,} of the third side?

The triangle inequality requires ∣14−5∣<x<14+5.|14 - 5| < x < 14 + 5\textsf{.} Simplifying gives 9<x<19.9 < x < 19\textsf{.}

Mid-gameeasy

In a triangle, two sides each have length 8.8\textsf{.} Which inequality represents the possible lengths, x,x\textsf{,} of the third side?

The triangle inequality requires ∣8−8∣<x<8+8.|8 - 8| < x < 8 + 8\textsf{.} Simplifying gives 0<x<16.0 < x < 16\textsf{.}

Mid-gamemedium

In a triangle, two sides each have length 10.10\textsf{.} Which inequality represents the possible lengths, x,x\textsf{,} of the third side?

The triangle inequality requires ∣10−10∣<x<10+10.|10 - 10| < x < 10 + 10\textsf{.} Simplifying gives 0<x<20.0 < x < 20\textsf{.}

Mid-gamemedium

A triangle has sides of length 99 and 20.20\textsf{.} Which inequality represents the possible lengths, x,x\textsf{,} of the remaining side?

The triangle inequality requires ∣20−9∣<x<20+9.|20 - 9| < x < 20 + 9\textsf{.} Simplifying gives 11<x<29.11 < x < 29\textsf{.}

Buzzer beatermedium

Two sides of a triangle measure 1616 and 9.9\textsf{.} Which inequality gives the possible lengths, x,x\textsf{,} of the third side?

The triangle inequality requires ∣16−9∣<x<16+9.|16 - 9| < x < 16 + 9\textsf{.} Simplifying gives 7<x<25.7 < x < 25\textsf{.}

Overtime

2 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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Tests that cover triangle inequality:
SBACPSAT 8/9i-ReadyNC EOG/EOCVTCAP
More Grade 7 skills
Make devices fair from experimental resultsRatio, rate, and proportion word problemsSum of consecutive integers (ACT)Compound probabilityEffect of scale factor on similar figuresOne-event probability word problemsPercent proportion word problemsRatios, rates, and proportionsAll Grade 7 practice →

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