Question
State whether the following triangle exists.
✓
Answer
No, the given triangle does not exist, since it does not satisfy the triangle inequality.
In the given $\triangle A B C$,
$\overline{A B}=24$ $cm, \overline{A C}=12$ $cm, \overline{B C}=11$ $cm$
Now $\overline{A C}+\overline{B C}=12+11=23$
and $\quad \overline{A B}=24$ $cm$
$\therefore \quad \overline{A C}+\overline{B C}<\overline{A B}$
Hence, the given triangle does not exist.
In the given $\triangle A B C$,
$\overline{A B}=24$ $cm, \overline{A C}=12$ $cm, \overline{B C}=11$ $cm$
Now $\overline{A C}+\overline{B C}=12+11=23$
and $\quad \overline{A B}=24$ $cm$
$\therefore \quad \overline{A C}+\overline{B C}<\overline{A B}$
Hence, the given triangle does not exist.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find six rational numbers between $\frac{-4}{8}\text{ and }\frac{3}{8}$
→Multiply the following fractions.
$6 \frac{2}{5} \times \frac{7}{9}$
→$6 \frac{2}{5} \times \frac{7}{9}$
Express the following numbers in standard form.
39087.8
39087.8
Copy the following on squared paper. Complete them so that the blue line is a line of symmetry.
Find the area of the triangle:
Find the percentage of children of different heights for the following data
| Height | Number of Children | In Fraction | In Percentage |
| 110cm | 22 | - | - |
| 120cm | 25 | - | - |
| 128cm | 32 | - | - |
| 130cm | 21 | - | - |
| Total | 100 | - | - |
Write the numerical coefficient of the following:
xy
xy
Raj travels $360\ km$ on three fifths of his petrol tank. How far would he travel at the same rate with a full tank of petrol$?$
→Find the area of the triangle in which Base $= 42\ cm$ and height $= 25\ cm.$
→Divide:
217.44 by 18
217.44 by 18