Properties of Triangles

If $∆\mathrm{ABC}$ is an equilateral triangle and $D$ is a point on $BC$ such that $AD\perp BC$, then find the ratio of $AB : BD$.

What is the ratio of side and height of an equilateral triangle?

If the altitude of an equilateral triangle is $\sqrt{6 } \mathrm{cm}$, its area (in ${\mathrm{cm}}^2$) is _____

If $D$ is a point on the side $BC$ of a $∆\mathrm{ABC}$ such that $AD\perp BC$ and $E$ is a point on $AD$ for which $AE : ED = 5 : 1$ ,If $\angle BAD=30°$ and $\tan \left(ACB\right)= 6 \tan \left(DBE\right)$, then find the value of $\angle \left(ACB\right)$.

$∆\mathrm{ABC}$ is an equilateral triangle with side $18 \mathrm{cm}.$D is a point on BC such that BD$=\frac{1}{3}\mathrm{BC}$ . Then length (in cm) of A D is:

The sum of all the three sides of an equilateral triangle is $15\sqrt{3} \mathrm{cm}$. The height of the triangle is_____.

I have three sides. One of my angle measure $60°$. Another has a measure of $60°$. What kind of a polygon am I? If I am a triangle, then what kind of triangle am I?

The sides of an equilateral triangle are shortened by $12 \mathrm{units} 13 \mathrm{units} \text{and} 14 \mathrm{units}$respectively and a right angle triangle is formed. The side of the equilateral triangle is _____.

A square is inscribed in a circle of radius$6\surd 2$ cm. Then a circle is inscribed in the square. Finally, an equilateral triangle is inscribed in the smaller circle. What is the area of the triangle (in sq. cm)?

Directions: Each of the questions below is followed by two statements, labeled (1) and (2), in which certain data are given. In these questions, you do not actually have to compute an the answer, but rather decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements 'plus' your knowledge of mathematics and everyday facts (such as the number of days in July), you are to choose the answer as per the options given below.

In trapezoid ABCD, what is the length of AB?

$\left(1\right) \mathrm{x}=\mathrm{y}=\mathrm{z}$

$\left(2\right) \mathrm{EB}=6$

The area of an equilateral triangle is $400\sqrt{3} {\mathrm{m}}^2$. Its perimeter is:

The angles adjacent to side $DE$ are

$\mathrm{ABC}$ and $\mathrm{BDE}$ are two equilateral triangles such that $\mathrm{D}$ is the mid-point of $\mathrm{BC}$. If the area of triangle $\mathrm{ABC}$ is $136 {\mathrm{cm}}^2$, then the area of triangle $\mathrm{BDE}$ is equal to:

Perimeter of an equilateral triangle, whose each side is $‘x’ \mathrm{unit}$ is _______.

All sides of an equilateral traingle are equal.

$O$ Is The Centre of circle$PQ$ Is diameter , $RS$ Is equal to $OP$ ,$PR$ and $QS$ produced meet at$A$.  Find the value of $\angle PAQ$.

$S$ is a point on the side $QR$ Of $△PQR$a , Such that $PS\perp QR$. $E$ is a point on $PS$ for which $PE:ES=5:1$. If $\angle QPS =30$ and$\tan \angle PRQ=6 \tan \angle SQE$. Find $\angle PRQ$ .

What can we say about the third side of the triangle of length 6 cm and 14 cm?

If all three side of a triangle are equal, then all the angles will be acute angle. Write "Yes" or "No" as final answer.

$16$ lines form $8$ equilateral triangles as shown in the figure.

Remove four lines from the above figure to form four equilateral triangles.