Question

The length of the side of a triangle are 5cm,12cm and 13cm.find the length of perpendicular form the opposite vertex to the side whose length is 13cm.​

Answer 1

area of the triangle is

$= \sqrt{15(15 - 5)(15 - 12)(15 - 13)} \\ = \sqrt{15 \times 10 \times 3 \times 2 } \\ = \sqrt{3 \times 5 \times 5 \times 2 \times 3 \times 2} \\ = 2 \times 5 \times 3 \\ = 30 \: cm {}^{2}$

now ..the area of the triangle is....

$area = \frac{1}{2} \times base \times height \\ = > height = \frac{2 \times area}{base} \\ = > height = \frac{2 \times 30}{13} = \frac{60}{13} cm$

the hieght is the perpendicular distance from the vertex to the side 13 cm.....

Answer 2

Answer:

area of triangle= √s(s-a) (s-b) (s-c)

Step-by-step explanation:

s=a+b+c/2

a=13

b=12

c=5

s=30/2=15

Area =√15(2)(3)(10)

=√3×5×2×3×2×5

=3×5×2

=30cm^2

Area of triangle=1/2×base×height

base=13cm

height=area of∆×2/base

= 30×2/13

=60/13 cm

Height of triangle=60/13cm

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