Triangle inequality Practice Questions (Grade 7)

Warm-upeasy

A triangle has sides of length $4$ and $11\textsf{.}$ Which inequality represents the possible lengths, $x\textsf{,}$ of the remaining side?

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

Mid-gameeasy

A triangle has side lengths $7$ and $3\textsf{.}$ Which inequality represents the possible lengths, $x\textsf{,}$ of the third side?

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

Mid-gameeasy

Two sides of a triangle measure $13$ and $6\textsf{.}$ Which inequality gives the possible lengths, $x\textsf{,}$ of the third side?

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

Mid-gameeasy

A triangle has side lengths $14$ and $5\textsf{.}$ Which inequality represents the possible lengths, $x\textsf{,}$ of the third side?

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

Mid-gameeasy

In a triangle, two sides each have length $8\textsf{.}$ Which inequality represents the possible lengths, $x\textsf{,}$ of the third side?

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

Mid-gamemedium

In a triangle, two sides each have length $10\textsf{.}$ Which inequality represents the possible lengths, $x\textsf{,}$ of the third side?

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

Mid-gamemedium

A triangle has sides of length $9$ and $20\textsf{.}$ Which inequality represents the possible lengths, $x\textsf{,}$ of the remaining side?

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

Buzzer beatermedium

Two sides of a triangle measure $16$ and $9\textsf{.}$ Which inequality gives the possible lengths, $x\textsf{,}$ of the third side?

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

Triangle inequality. Game on.