Question

Find area of triangle,two sides of which are 8 cm and 11 cm and perimeter is 32 cm

Answer 1

Answer:-

Perimeter of Triangle = Sum of all Sides of a Triangle .

32=11+8+c

c=32-(11+8)

c=32-19

c=13cm

To find the area in this case we should Heron's Formula

area=√s(s-a)(s-b)(s-c) (Root over full)

s=)semi perimeter

a=11 , b=8 , c=13 .

s=(a+b+c)÷2

s=)(11+8+13)÷2

=)32÷2

=)16

Area:-

√16×(16-11)(16-8)(16-13) (Root over full)

√16×(5)(8)(3) (Root over full)

√16×120 (Root over full)

√1920

=)8√30

*Therefore the area of a triangle of length of two sides are 11 , 8 and with a perimeter of 32 .

Hope it helps you .

Answer 2

$\bf{ \underline{ \underline{Answer \: : }}} \:$

$\large\bold\red{Answer~is~8\sqrt{30}~.}$

$\bf{ \underline{ \underline{Explanation \: : }}} \:$

● We know that Perimeter :-

sum of sides.

$32 = 11 + 8 + c \\ \\ 32 - 19 = c \\ \\ c = 13 \: cm$

● For area use Herons formula.

Semiperimeter :-

$⟹ \frac{32}{2} = 16 \: cm$

Area :-

$= \sqrt{s(s - a)(s - b)(s - c ) \: } \\ \\ \\ = \sqrt{16 \times 5 \times 3 \times 8} \\ \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 5 \times 3 \times 2 \times 2 \times 2} \\ \\ = 2 \times 2 \times 2 \sqrt{5 \times 3 \times 2} \\ \\ \bf{ \underline{ \underline{ = { 8 \sqrt{30}} }}}$

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