In triangle ABC, the bisector of angle BAC cuts the side BC at D. If AB = 10 cm, and AC = 14 cm, then what is BD : DC ?

Two triangles, MNO and XYZ are given similar with the ratio of their side as 9 : 4. If the area of the larger triangle is 243 sq. cm, then the area of the smaller triangle will be:

∆XYZ and ∆PQR are similar. XY : PQ = 6 : 1. Area of ∆PQR is 6 cm². What is the area of ∆XYZ?

In triangle ABC, the straight line parallel to the side BC meets AB and AC at the points P and Q, respectively. If AP=QC, the length of AB is 16 cm and the length of AQ is 4 cm, the length (in cm) of CQ is :

Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have a radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is

In △XYZ, if XY = 5 cm, XZ = 7 cm and Q is a point on YZ such that XQ bisects ∠X, then YQ : QZ is:

In a triangle DEF, DP is the bisector of ∠D, meeting EF at P. If DE = 14 cm, DF = 21 cm, and EF = 9 cm, find EP.

The area of an equilateral triangle is 4\(\sqrt{3}\) cm². Find the side (in cm) of the triangle.

In the given figure, if AD⊥BC, AC = 26 units, CD = 10 units, BC= 42 units, ∠DAC = x and ∠B = y, then the value \(\frac{6}{cosx}-\frac{5}{cosy}+8tany\)

The length of each side of an equilateral triangle is 22 cm. Find the area (in cm²) of this triangle.

The lengths of the three sides of a triangle are 30 cm, 42 cm and x cm. Which of the following is correct?

What is the radius of the circle that circumscribes the triangle ABC whose sides are 16, 30, and 34 units, respectively?

In an isosceles triangle, if the unequal side is 8 cm and equal side is 5 cm. then the area of the triangle is:

ΔΑΒΟ - ΔDEF and the perimeters of ΔABC and ΔDEF are 40 cm and 12 cm, respectively. If DE = 6 cm, then AB is:

If in △ XYZ, XY = 4 and XZ = 5 cm, and Q is a point on YZ such that XQ bisects ∠X, then YQ : QZ is:

Let A, B, C be the mid-points of sides PQ, QR PR, respectively, of \(\triangle\)PQR, If the area of \(\triangle\)PQR is 32 cm², then find the area of \(\triangle\)ABC.

D and E are points on the sides AB and AC, respectively, of △ABC such that DE is parallel to BC and AD: DB-7:9. If CD and BE intersect each other at F. then find the ratio of areas of △DEF and △CBF.

Which of the following statements is NOT true?

The three sides of a triangle are 12, 17 and x units. Which of the following options is correct?

The sides of two similar triangles are in the ratio 5 : 7. The areas of these triangles are in the ratio:

If ∆ABC ~ ∆PQR, AB = 4 cm, PQ = 6 cm, QR = 9 cm, and RP = 12 cm, then find the perimeter of ∆ABC.

The perimeter of an equilateral triangle is 48 cm. Find its area (in cm²)

The mid points of AB and AC of a △ABC are X and Y, respectively. If BC + XY = 18 units, then the value of BC - XY is :

The area of the two triangles is in the ratio 5 : 3 and their height is in the ratio 5 : 7. Find the ratio of their base.

If \(\triangle \)ABC is right-angled at B, AB = 12 cm, and \(\angle\)CAB = 60°, determine the length of BC.

If the areas of two similar triangles are in the ratio 196 : 625, what would be the ratio of the corresponding sides?

In a ΔABC, DE || BC, where D is a point on AB and E is a point on AC. If DE divides the area of ΔABC into two equal parts, then DB : AB is equal to:

The perimeter of an isosceles triangle is 100 cm. If the base is 36 cm, then find its semi perimeter (in centimetres).

The ratio of the length of each equal side and the third side of an isosceles triangle is 3 : 5. If the area of the triangle is 30\(\sqrt{11}\) cm², then the length of the third side (in cm) is:

A triangle ABC has sides 73 cm, 55 cm, and 48 cm.

(I) It's not a right-angle triangle.

(II) Area of the triangle ABC is 1302 cm²

(III) If a circle is inscribed inside a circle having radius r then, the value of r will be 12 cm.

The lengths of sides of a triangle are in the ratio 3 : 4 : 5. If the perimeter of the triangle is 72 cm, find the length of the largest side.

Quantity I: Two sides of a triangle are equal to 16 cm and two angles of triangles are also equal(one corresponding angle and one other). Find the area of that triangle.

Quantity II: The area of the square is 576 cm. Find the area of the square formed by joining the midpoint of the sides.

The area of a right triangle 30 cm². If the base of the triangle is 7 cm less than its height, then find the length of base of the triangle.

The perimeter of an equilateral triangle PQR is 417 cm.

(I) Side = 139 cm

(II) Height = 69.5√3 cm

(III) If the side of the equilateral triangle is equal to the length of a rectangle whose area is 15568 cm² then, its breadth will be 112 cm.

Find the area of the triangle whose three sides are 32 cm, 36 cm and 28 cm respectively.

The ratio of corresponding sides of two similar triangle is √5 : √6. Find the ratio of the areas of the two triangles.

The ratio between perimeter of an equilateral triangle and a square is 3 : 8. The area of square is 800% of area of a rectangle having sides 8 m and 4 m. Find the perimeter of triangle.

The area of a right angled triangle is 84 cm² and one of its perpendicular sides is 24 cm. If the perimeter of a square is equal to the perimeter of the triangle, what is the area (in cm²) of the square?

What is the height of the triangle?

Statement I: The area of the triangle is 20 times its base.

Statement II: The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.

The perpendicular height of the equilateral triangle is \(6 \sqrt{3}\) cm. Find the area of the triangle.

Find the area of the shaded region, if AN = 4 cm, NC = 8 cm and AB = BC.

A circle, with radius 8 cm, which has the area equal to the area of a triangle with base 8 cm. Then the length of the corresponding altitude of triangle is :

Find the length of the median of the triangle with sides 10 cm, 11 cm, and 12 cm respectively. (Median bisects the side of 12 cm)

The areas of two squares are 16:9. The ratio of their perimeter is :

PQRS is a trapezium in which PQ is parallel to RS and PQ = 4(RS). The diagonals of the trapezium intersect at O. What is the ratio of the area of triangle SRO to the area of the triangle PQO?

ABC is an isosceles triangle with AB = AC. Line AD divides angle BAC such that BAD = DAC, Find BC : DC?

In the figure below, p, q, and r are three parallel lines. Distances between lines p and q and lines q and r are in the ratio 3: 4. If the area of the triangle ABE is 27 sq. cm. Then what is the area of the triangle FCD (in sq. cm)?

A square is drawn on diagonal AC of a regular hexagon ABCDEF. Length of side of hexagon is 8√3 cm. Find the area of square.

In the figure given below, on one of the sides (BC) on the triangle ABC two points D and E are chosen such that BD : DE : EC = 5 : 3 : 2. A line parallel to the side AB is drawn passing through E such that it meets AD produced at F. If area of the triangle ABC is 250 cm², then what is the area of the triangle EFD (in cm²)