What is meant by adjacent sides?

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In mathematics and geometry, adjacent sides refer to sides that share a common endpoint or vertex. Adjacent sides can be found in various two-dimensional shapes, such as squares, rectangles, triangles, and polygons.

For example, in a square, each of the four sides is adjacent to the two sides it touches. In a rectangle, two sides that are opposite each other are referred to as "opposite sides," while the other two sides are considered to be adjacent. Any two sides that share a common vertex are considered to be adjacent sides in a triangle.

Adjacent sides play an important role in many geometric calculations and measurements, such as finding the perimeter of a shape, calculating the area, and determining the interior and exterior angles of a shape. By understanding the relationships between adjacent sides, it is possible to make more precise calculations and predictions about various shapes and figures.

Adjacent Sides

Adjacent Sides

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CBSE CLASS XII Related Questions

1.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

View Solution

2.
Find the vector and cartesian equations of the line passing through the point of intersection of the lines \( \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) \) and \( \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) \) and parallel to the line \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).

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3.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

\(-\frac{\pi}{2}\)
\(-\frac{\pi}{4}\)
\(\frac{\pi}{4}\)
\(\frac{\pi}{2}\)

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4.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :

5.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

\(0\)
\(-2\)
\(-1\)
\(2\)

View Solution

6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

View Solution

What is meant by adjacent sides?

CBSE CLASS XII Related Questions

1.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

3.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

4.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :

5.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

Comments

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What is meant by adjacent sides?

CBSE CLASS XII Related Questions

1.Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

3. Find: The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

4.At a birthday party, children are being served orange juice in conical cups, as shown in the figure. Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.On the basis of the above information, answer the following questions :

5. Find: If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

6.Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).

3.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

4.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :

5.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).

6.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]