Question

the length of the sides of a triangle are 33 cm 44 cm and 55 CM respectively find the area of the triangle and hence find the height corresponding of the side measuring 44 cm

Answer 1

Answer:

Step-by-step explanasemiperimeter = (33 + 44 + 55)/2

= 66 cm

use hero's formula ,

area of triangle =root {66 (66- 33)(66-44)(66-55)}

=root {66 x 33 x 22 x 11 }

=11 x 11 x 6 = 121 x 6 = 726 cm^2

area of triangle = 1/2 height x base

726 = 1/2 height x 44

height = 726/22 =33 cm

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Answer 2

Answer:

$Area \ = \bold{726}\ cm^2 \\ \\ \\ Height \ = \bold{33}\ cm$

Step-by-step explanation:

$s = \frac{33 + 44 + 55}{2} = \frac{132}{2} =\  66 \\ \\ \\ Area \\ \\ = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{66(66 - 33)(66 - 44)(66 - 55)} \\ \\ = \sqrt{66 \times33 \times 22 \times 11} \\ \\ = \sqrt{11 \times 6 \times 11 \times 3 \times 11 \times 2 \times 11} \\ \\ = \sqrt{11 \times 11 \times 11 \times 11 \times 6 \times 3 \times 2} \\ \\ = \sqrt{11 \times 11 \times 11 \times 11 \times 3 \times 2 \times 3 \times 2}$

$\\ \\ = \sqrt{11 \times 11 \times 11 \times 11 \times 3 \times 3 \times 2 \times 2} \\ \\ = 11 \times 11 \times 3 \times 2 \\ \\ = \bold{726} \\ \\ \\ \therefore\ Area \ = \bold{726}\ cm^2$

$Let the height corresponding to the side measuring 44 cm be \ h. \\ \\ \\ Area \\ \\ = \frac{1}{2} \times 44 \times h = 726 \\ \\ = 22h = 726 \\ \\ h = \frac{726}{22} = \bold{33} \\ \\ \\ \therefore\ The height is \ \bold{33}\ cm.$

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