Examples (Revised) - Chapter 6 - Triangles & Its Properties - Ncert Solutions class 7 - Maths

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Chapter 6 - Triangles & Its Properties | NCERT Solutions Class 7 Maths

Example 1

Find angle $x$ in Fig 6.11.
Solution

Sum of interior opposite angles $=$ Exterior angle or

$
\begin{aligned}
50^{\circ}+x & =110^{\circ} \\
x & =60^{\circ}
\end{aligned}
$

Example 2

In the given figure (Fig 6.18) find $\mathrm{m} \angle \mathrm{P}$.
Solution

By angle sum property of a triangle,

$
\mathrm{m} \angle \mathrm{P}+47^{\circ}+52^{\circ}=180^{\circ}
$

Therefore
$
\begin{aligned}
\mathrm{m} \angle \mathrm{P} & =180^{\circ}-47^{\circ}-52^{\circ} \\
& =180^{\circ}-99^{\circ}=81^{\circ}
\end{aligned}
$

Example 3

Is there a triangle whose sides have lengths $10.2 \mathrm{~cm}, 5.8 \mathrm{~cm}$ and $4.5 \mathrm{~cm}$ ?
Solution

Suppose such a triangle is possible. Then the sum of the lengths of any two sides would be greater than the length of the third side. Let us check this.
\begin{tabular}{ll} 
Is $4.5+5.8>10.2 ?$ & Yes \\
Is $5.8+10.2>4.5 ?$ & Yes \\
Is $10.2+4.5>5.8 ?$ & Yes
\end{tabular}

Therefore, the triangle is possible.
Example 4

The lengths of two sides of a triangle are $6 \mathrm{~cm}$ and $8 \mathrm{~cm}$. Between which two numbers can length of the third side fall?

Solution

We know that the sum of two sides of a triangle is always greater than the third.
Therefore, third side has to be less than the sum of the two sides. The third side is thus, less than $8+6=14 \mathrm{~cm}$.

The side cannot be less than the difference of the two sides. Thus, the third side has to be more than $8-6=2 \mathrm{~cm}$.
The length of the third side could be any length greater than 2 and less than $14 \mathrm{~cm}$.

Example 5

Determine whether the triangle whose lengths of sides are $3 \mathrm{~cm}, 4 \mathrm{~cm}$, $5 \mathrm{~cm}$ is a right-angled triangle.

Solution

$3^2=3 \times 3=9 ; 4^2=4 \times 4=16 ; 5^2=5 \times 5=25$
We find $3^2+4^2=5^2$.
Therefore, the triangle is right-angled.
Note: In any right-angled triangle, the hypotenuse happens to be the longest side. In this example, the side with length $5 \mathrm{~cm}$ is the hypotenuse.

Example 6

$\Delta \mathrm{ABC}$ is right-angled at $\mathrm{C}$. If $\mathrm{AC}=5 \mathrm{~cm}$ and $\mathrm{BC}=12 \mathrm{~cm}$ find the length of $A B$.

Solution

A rough figure will help us 

By Pythagoras property,
$
\begin{aligned}
\mathrm{AB}^2 & =\mathrm{AC}^2+\mathrm{BC}^2 \\
& =5^2+12^2=25+144=169=13^2 \\
\mathrm{AB}^2 & =13^2 . \text { So, } \mathrm{AB}=13
\end{aligned}
$
or
or the length of $A B$ is $13 \mathrm{~cm}$.
Note: To identify perfect squares, you may use prime factorisation technique.