Question

find the arae of a triangle, two sides of which are 8cm and 11cm and the perimeter is 32cm .​

Answer 1

Answer:

if sum of two sides is 19 and perimeter is 32 then third side is 13 hence using herons formula we can get our area hope it helps you

Answer 2

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{GIVEN:-}$

★Two sides of the triangle = 8 cm and 11 cm.

★Perimeter = 32 cm.

$\underline \mathbb{TO \: FIND:-}$

★Area of the triangle.

$\underline \mathbb{FORMULA:-}$

★Sum of the 3 sides of a triangle = Perimeter.

$★Area \: of \: the \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \: (where \: s \: is \: semi \: perimeter \\ \: and \: a \: ,\: b \: and \: c \: are \: sides \: of \: the \: triangle.)$

$★semi \: perimeter \: = > \frac{a + b + c}{2} = > \frac{perimeter}{2}$

$\underline \mathbb{ASSUMPTION:-}$

Let, the 1st side of the triangle(a) = 8 cm

Let, the 2nd side of the triangle (b)= 11 cm

Let, the 3rd side of the triangle (c)= c cm

$\underline \mathbb{BY \: THE \: PROBLEM:-}$

Sum of the 3 sides of a triangle = Perimeter.

(a+b+c) = 32

(8+11+c) = 32

(19+c) = 32

c = 32 - 19

(Third side) c = 13 cm

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$semi \: perimeter \: = > \frac{a + b + c}{2} = > \frac{perimeter}{2} \\ \\ \implies \: perimeter = \frac{32}{2} = 16 \: cm$

------------------------------------------------------------------------

$Area \: of \: the \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \implies \: \sqrt{16 (16 - 8)(16 - 11)(16 - 13)} \\ \\ \implies \: \sqrt{16 \times 8 \times 5 \times 3} \\ \\ \implies \: \sqrt{8 \times 2 \times 8 \times 5 \times 3} \\ \\ \implies \: 8\sqrt{30} \: {cm}^{2}$

$\underline \mathbb{ANSWER:-}$

$\boxed{8 \sqrt{30} {cm}^{2} }$