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Practice Triangle Questions and Answers

The perimeter of an equilateral triangle is 48√3 cm. Find its height.
If the ratio of the area of two similar triangles is √3:√2 then what is the ratio of the corresponding sides of the two triangles? ...
The area of a triangle is 216 cm² and the ratio of its sides is 9: 12: 15. What is the perimeter of the triangle?
If the side of an equilateral triangle is 12cm, then find the area (in cm 2 ) of the triangle (correct to two decimal places).
The area of a triangle is 480 cm² and the ratio of its sides is 10: 24: 26. What is the perimeter of the triangle?
In a triangle ABC, the incenter is at O. Find angle BAC if angle BOC=120°.
If the inradius of a triangle with a perimeter of 60cm is 8 cm, then find the area of the triangle.(in cm2)
Two triangles DEF and XYZ are similar to each other. If DE = 5 cm, DF = 7 cm, and XY = 15 cm, then find XZ.
Two triangles DEF and XYZ are congruent to each other such that DE = 10 cm, YZ = 24 cm, and ∠DEF = ∠XYZ = 90⁰. Find the circumradius of ΔDEF....
An equilateral triangle ABC is surmounted on a square BCDE whose area is 500 cm². Find the altitude of triangle ABC.
In a triangle ABC, AD is the altitude from A to BC. If AD = 12 cm, AB = 13 cm, and AC = 14 cm, find the length of BC.
The base of a triangular plot is 25 meters, and its height is 30 meters. If a path of 2 meters wide is to be built around the plot, what will be the area o...
In a right triangle, if the altitude drawn to the hypotenuse divides the triangle into two triangles of equal area, what is the value of the smallest angle...
A triangle XYZ is drawn inside a circle with a radius of 8 cm, such that its vertices lie on the circumference of the circle. Given that ∠XYZ = ∠YZX = ...
In a right-angled triangle, the hypotenuse is 20 cm, and one of the legs is 12 cm. Find the area of the triangle.
In a triangle, the lengths of two sides are 13 cm and 14 cm, and the included angle between them is 60°. Find the area of the triangle.
In a right-angled triangle, the perimeter is 60 cm. If the base is 12 cm and the height is 16 cm, find the length of the hypotenuse.
In a right-angled triangle, the length of the hypotenuse is 25 cm, and the perimeter is 60 cm. Find the area of the triangle.
The base of an isosceles triangle is 20 cm, and the sum of the other two sides is 30 cm. Find the area of the triangle.
Two sides of a triangle are 10 cm and 15 cm. Which of the following can be the third side of the triangle?
In an equilateral triangle, the length of the side is 18 cm. A circle is inscribed in the triangle. Find the radius of the circle.
In a right-angled triangle, the legs are in the ratio 3:4, and the hypotenuse is 25 cm. Find the perimeter of the triangle.
In a triangle ABC, the lengths of sides AB, BC, and AC are 13 cm, 14 cm, and 15 cm, respectively. Find the area of the triangle.
A right-angled triangle has an area of 120 m², and the ratio of its base to height is 5:3. The side length of an equilateral triangle is 125% of the avera...
In triangle ABC, the difference between angle A and angle B is 16°, and the difference between angle A and angle C is 8°. Determine the measure of angle ...
The area of an isosceles triangle ABC is 8√5 cm². In this triangle, sides AB and BC are equal in length, and the base AC has a length of 8 cm. Determine...
Determine the area of the triangle whose vertices lie on the co-ordinates (2, 4), (4, 2), (-2, -5)
The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is the area of the triangle?
The side of an equilateral triangle is 15 cm long. What is the radius of the circle circumscribing this equilateral triangle?
Find the area of the triangle formed by the line 5x + 3y = 15 and the x-axis and the y-axis.
A right-angled triangle has one leg of 12 cm and the hypotenuse of 13 cm. Find the length of the other leg.
The vertices of a triangle are given as (5, 4), (9, 6), and (1, 5). Determine the area enclosed by this triangle.
In triangle ABC, the lengths of its sides are given as AB = 8 cm, AC = 10 cm, and BC = 12 cm. Determine the length of the median drawn from vertex 'A' to t...
In triangle △ ABC, the internal angle bisectors of ∠ B and ∠ C intersect at point OO. If the measure of ∠ BAC = 50o , determine the measure of ∠ ...
A triangle has sides 13 cm, 14 cm, and 15 cm. Find the area of the triangle.
The sides of a triangle are 15 cm, 20 cm, and 25 cm. A smaller triangle is drawn inside it such that its sides are proportional to the original triangle an...
The area of an equilateral triangle increases by 16√3 square units when the length of each side is increased by 4 units. What is the original perimeter o...
In a ΔDEF, ∠D = 45°, ∠E = 2∠F. What is the value of ∠F?
Determine the inradius of an equilateral triangle whose altitude measures 9√3 cm.
The area of an equilateral triangle is 64√3 cm2. Find the radius of the circle that circumscribes the triangle.

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