Question

find the area of triangle whose sides are 15 cm and 8cm 17 cm find the length of the altitude corresponding to the largest side of a triangle
pls give step by step answer....​

Answer 1

Solution :-

Lets first check if its a right triangle or not.

→ Base² + Perpendicular² = Hypotenuse²

→ 15² + 8² = 17²

→ 225 + 64 = 289

→ 289 = 289

So, we can conclude that given triangle is a right angle ∆ .

Now,

→ Area of Right angle ∆ = (1/2) * Base * Perpendicular

→ Required Area = (1/2) * 15 * 8 = 60cm² (Ans.)

Now, Let us assume that length of the altitude corresponding to the largest side of a triangle that is hypotenuse of ∆ is x cm.

Than ,

→ Base of ∆ = Hypotenuse = 17cm.

→ Altitude = x cm.

→ Area = 60cm²

Comparing area we get,

→ (1/2) * Base * Altitude = 60

→ (1/2) * 17 * x = 60

→ 17x = 120

→ x = (120/17) cm (Ans.)

Hence, Area of given ∆ is 60cm² and length of the Altitude corresponding to the Largest side of the ∆ is (120/17)cm.

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Note :- we can find area of ∆ by Heron's formula also.

Area of ∆ with three sides length as a,b and c and semi-perimeter as s is given by :-

• √[s(s-a)(s-b)(s-c)]

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