Test Details

The Triangle and Its Properties

Jan 27, 5:00 PM

45 minutes

Jan 27, 5:45 PM

50.0 marks

MCQ

25 questions

Shiv Anand

Class Details

Maths

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Question Text

Question 1 :
If the two legs of a right angled triangle are equal and the square of the hypotenuse is $100cm^2$, then the length of each leg is _________.

Question 2 :
What is the length of the hypotenuse formed if the two sides are of 5 cm, 12 cm?

Question 3 :
 If the two legs of a right angled $\Delta$ are equal and the square of the hypotenuse is $100,$ then the length of each leg is:

Question 4 :
Find the perimeter of an isosceles right triangle with each of its congruent sides is $7\,cm$.

Question 5 :
If two sides of an isosceles $\Delta$ Ie are $3$ cm and $8$ cm, then the length of the third side is

Question 7 :
Find hypotenuse of right angled triangle if the sides are $12,4\sqrt 3$

Question 9 :
How many isosceles triangles are there with$\displaystyle { 40 }^{ o }$ as oneof the three angles?

Question 10 :
If two altitudes of a triangle are equal in length, then the triangle is

Question 11 :
A triangle has side lengths of $6$ inches and $9$ inches. If the third side is an integer, calculate the minimum possible perimeter of the triangle (in inches).

Question 12 :
Each of the equal sides of an isosceles triangle is $2$ cm more than its height and the based of the triangle is $12$ cm. Find the area of the triangle.

Question 13 :
The sides of a right triangle are $(x-1)$, $x$ and $(x+1)$. Find the sides of the triangle.

Question 14 :
In $\Delta ABC, A = 50^{\circ}, \angle B = 60^{\circ}$, arranging the sides of the triangle in ascending order, we get :

Question 15 :
The length of two sides of a triangle is $7 \,cm$ and $9 \,cm$. the length of the third side may lie between

Question 17 :
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is

Question 18 :
A certain right angled triangle has its area numerically equal to its perimeter. The length of its each side is an even integer. What is the perimeter?

Question 19 :
If a triangle $PQR$ has been constructed taking $QR = 6 $ cm, $PQ = 3 $ cm and $PR = 4 $ cm, then the correct order of the angle of triangle is

Question 20 :
The lengths of the sides of a right triangle are $5x + 2$, $5x$ and $3x - 1$. If $x > 0$ then the length of each side is?

Question 21 :
In $\displaystyle \Delta ABC,$ segments $AD, BE$ and $CF$ are the altitudes. If $AB \times AC = 28.80$ and $BE \times CF = 20,$ then $AD \times BC$ equals:

Question 22 :
On the sides of an arbitrary triangle ABC, triangles BPC, CQA, and ARB are externally erected such that $\angle{PBC}=\angle{CAQ}=45^{\circ}$, $\angle{BCP}=\angle {QCA}=30^{\circ}$, $\angle{ABR}=\angle{BAR}=15^{\circ}$;

Question 23 :
The radii of described circle of $\triangle {ABC}$ are ${r}_{1}, {r}_{2}$ and ${r}_{3}$ respectively (opposite to vertices $A,B$ and $C$). If ${r}_{2}+{r}_{3}=2R$ and ${r}_{1}+{r}_{2}=3R$ then

Question 24 :
The product of the arithmetic mean of the lengths of the sides of a triangle and harmonic mean of the lengths of the altitudes of the triangle is equal to

Question 25 :
The measures of the angles of $\triangle QRS$ are $m\angle Q = 2x + 4, m\angle R = 4x - 12,$ and $m\angle S = 3x+8.$ $QR = y + 9, RS = 2y-7$, and $QS = 3y-13.$ The perimeter of $\triangle QRS$ is:

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