The perimeter of a triangle is 50 cm. one side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. find the area of the triangle.

Fig. 12.4 2. The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle. 3. The area of a trapezium is 475 cm 2 and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other. 4. A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed. 5. A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1 m 2 of the field, find the total cost of ploughing the field. 6. In Fig. 12.5, △ ABC has sides AB = 7.5 cm , AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of △ ABC is constructed. Find the height DF of the parallelogram. 7. The dimensions of a rectangle ABCD are 51 cm × 25 cm. A trapezium PQCD with its parallel Views: 5,894 ∠ POR = 12 3 ​ × 18 0 ′′ = 7 5 ∘ Vig. 6.9 Similarly, ∠ ROQ = 12 7 ​ × 18 0 ∘ = 10 5 ∘ Now. ∠ POS = ∠ ROQ = 10 5 − (Vertically opposite angles) ∠ SOQ = ∠ POR = 7 5 ∘ (Vertically opposite angles) *ayple 2 : In Fig. 6.10, ray OS stands on a line POQ. Ray OR and ray OT are angle bisec...

Step 1: Find the length of each sides of the triangle Given, perimeter of a triangle = 50 c m Let the smaller side be x . According to question, So , the remaining sides are 2 x - 6 c m and x + 4 c m . Given , Perimeter of the triangle = 50 c m . x + 2 x - 6 + x + 4 = 50 4 x - 2 = 50 4 x = 50 + 2 4 x = 52 x = 52 4 x = 13 So , the required sides of the triangle are x = 13 c m x + 4 = 13 + 4 = 17 c m 2 x - 6 = 2 × 13 - 6 = 26 - 6 = 20 c m Step 2: Use Heron's formula to find the area of triangle Area of the triangle = s s - a s - b ( s - c ) (where , a , b , c are sides of triangle and s is semi perimeter) Here, a = 13 cm , b = 17 cm , c = 20 cm s = a + b + c 2 = 13 + 17 + 20 2 = 50 2 = 25 c m Area of the triangle = 25 × 25 - 13 × 25 - 17 × 25 - 20 = 25 × 12 × 8 × 5 = 5 × 5 × 2 × 2 × 3 × 2 × 2 × 2 × 5 = 5 × 2 × 2 3 × 2 × 5 = 20 30 Hence , Area of the triangle is 20 30 c m 2 .

Step 1: Enter the values of any two angles and any one side of a triangle below which you want to solve for remaining angle and sides. Triangle calculator finds the values of remaining sides and angles by using Sine Law. Sine law states that a sin A = b sin B = c sin C Cosine law states that- a 2 = b 2 + c 2 - 2 b c . cos ( A ) b 2 = a 2 + c 2 - 2 a c . cos ( B ) c 2 = a 2 + b 2 - 2 a b . cos ( C ) Step 2: Click the blue arrow to submit. Choose "Solve the Triangle" from the topic selector and click to see the result in our Examples- Popular Problems- A = 4 5 , B = 5 2 , a = 1 5 a = 4 , b = 1 0 , c = 7 B = 1 2 7 , a = 3 2 , C = 2 5 B = 8 5 , C = 1 5 , b = 4 0 C = 3 , a = 1 6 , b = 3 3

a = ∠α = b = ∠β = c = h = A = area P = perimeter Related Right triangle A right triangle is a type of triangle that has one angle that measures 90°. Right triangles, and the relationships between their sides and angles, are the basis of trigonometry. In a right triangle, the side that is opposite of the 90° angle is the longest side of the triangle, and is called the hypotenuse. The sides of a right triangle are commonly referred to with the variables a, b, and c, where c is the hypotenuse and a and b are the lengths of the shorter sides. Their angles are also typically referred to using the capitalized letter corresponding to the side length: angle A for side a, angle B for side b, and angle C (for a right triangle this will be 90°) for side c, as shown below. In this calculator, the Greek symbols α (alpha) and β (beta) are used for the unknown angle measures. h refers to the altitude of the triangle, which is the length from the vertex of the right angle of the triangle to the hypotenuse of the triangle. The altitude divides the original triangle into two smaller, similar triangles that are also similar to the original triangle. If all three sides of a right triangle have lengths that are integers, it is known as a Pythagorean triangle. In a triangle of this type, the lengths of the three sides are collectively known as a Pythagorean triple. Examples include: 3, 4, 5; 5, 12, 13; 8, 15, 17, etc. Area and perimeter of a right triangle are calculated in the same way as any ...

SOLUTION Given, Let smaller side = a --------------- (i) one side = a + 4 --------------- (ii) third side = 2a - 6 --------------- (iii) On solving (i),(ii),(iii) we get = a + a + 4 + 2a - 6 =50 = 4a - 2 = 50 a = 13 Substituting a value in (i),(ii),(iii) smaller side = 13 one side = 17 third side = 20 s= 20 + 17 + 13 2 = 50 2 = 25 Area = √ s ( s − a ) ( s − b ) ( s − c ) = ( √ 25 ( 25 − 13 ) ( 25 − 17 ) ( 25 − 20 ) ) = 20 √ 30