Question

The sides of a triangle are 17 CM, 25cm and 26cm .The length of the altitude to the longest side correct Upto two places of decimal ​

Answer 1

Answer:

15.69

Step-by-step explanation:

Is the answer 1st find the area with Heron's formula and lenght of the altitude using area of triangle

Answer 2

Answer:

The length of the altitude to the longest side is 15.69 cm

Step-by-step explanation:

Given: The sides of the triangle are 17cm , 25cm and 26 cm

To find: The length of the altitude to the longest side

Solution:

The sides of the triangle are 17cm , 25cm and 26 cm

Area of the triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

Semi perimeter of triangle = $\frac{a+b+c}{2}$

a = 17 cm     b = 25 cm     c = 26 cm

Semi perimeter of triangle S = $\frac{17 + 25 + 26}{2}$

S = $\frac{68}{2}$

Semi perimeter of a triangle = 34 cm

Area of the triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

                                = $\sqrt{34(34 - 17)(34-25)(34-26)}$

                               = $\sqrt{34(17)(9)(8)}$

                               = $\sqrt{41616}$

                               =204 $cm^{2}$

Area of the triangle = 204 $cm^{2}$

we know that

Area of the triangle =  $\frac{1}{2} base (height)$

 204  =   1/2  × 17 × h

204   = 26/2 × h

h = (204 × 2) ÷ 26

h = 15.69 cm

The height of the altitude  = 15.69 cm

Final answer:

The length of the altitude to the longest side is 15.69 cm

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