Question

two sides of a triangle are 10 centimetre and 5 cm in length and the length of the median to the third side is 6.5 CM if the area of the triangle is 6 root p CM square find the value of p​

Answer 1

Step-by-step explanation:

Given  

two sides of a triangle are 10 centimetre and 5 cm in length and the length of the median to the third side is 6.5 CM if the area of the triangle is 6 root p CM square find the value of p​

• By inserting a line  we get
• Length of median = 1/2 √2 b^2 + 2 c^2 – a^2
•             6.5 / 0.5 = √2 x 5^2 + 2 x 10^2 – a^2
•      Squaring both sides we get
•           42.25 / 0.25 = 50 + 200 – a^2
•              169 = 250 – a^2
•              a ^2 = 250 – 169
•             a^2 = 81
•                So a = 9
• We know that S = a + b + c / 2
•                           = 10 + 5 + 9 / 2
•                           = 24 / 2
•                            = 12
• Now area of triangle = √ s(s – a) (s – b) (s – c) = 6√p
•                                   = √12(12 – 10) (12 – 5) (12 – 9)
•                                  = √12 x 2 x 7 x 3
•                                  = √36 x 2 x 7
•                                   = 6 √14 = 6√p
•                           Now p = 14

Answer 2

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