Question

The measurements of sides of a garden which is in the shape of a Scalene triangle are 40 m ,32 m and 24 m.The gardener wants to decorate the one of the kinds of concurrentlines ,namely altitudes of the triangle with green ribbon Question:2) What is the value of Range of these altitudes A) 12.8 B) 32 C)0​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given :- The measurements of sides of a garden which is in the shape of a Scalene triangle are 40 m ,32 m and 24 m.The gardener wants to decorate the one of the kinds of concurrent lines ,namely altitudes of the triangle with green ribbon .

To Find :- What is the value of Range of these altitudes A) 12.8 B) 32 C)0

Solution :-

→ semi perimeter of ∆ = (a + b + c)/2 = (40 + 32 + 24)/2 = 48

so,

→ Area of given ∆ = √[s * (s - a) * (s - b) * (s - c)] = √[48 * 8 * 16 * 24] = √(8 * 6 * 8 * 16 * 4 * 6) = √(8² * 8² * 6²) = 8 * 8 * 6 = 384 m² .

then,

→ Area = (1/2) * Base * Altitude = 384 m².

therefore,

→ Altitude on side 40 m :- (1/2) * 40 * Altitude = 384 => Altitude = 19.2 m

→ Altitude on side 32 m :- (1/2) * 32 * Altitude = 384 => Altitude = 24 m

→ Altitude on side 24 m :- (1/2) * 24 * Altitude = 384 => Altitude = 32 m

hence,

→ Range of these altitudes = Highest value - Lowest value = 32 - 19.2 = 12.8 m (A) (Ans.)

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