Question

find the area of a triangle with perimeter 22cm one side 9cm and difference of other two sides is 7cm pls tell

Answer 1

Given, one side of the triangle = 9 cm



Given, difference between other two sides of the triangle = 7 cm


length 2nd side - length of 3rd side = 7 cm ---- : ( 1 )



Given, perimeter of the triangle = 22 cm


Sum of lengths of all sides ( perimeter ) = 22 cm


Length of 1st side + length of 2nd side + length of 3rd side = 22 cm


9 cm + length of 2nd side + length of 3rd side = 22 cm


length of 2nd side + length of 3rd side = 22cm - 9cm


→ length of 2nd side + length of 3rd side = 13 cm



Now, let length of 2nd side = x and let the length of 3rd side be y



→ x + y = 13 cm -----: ( 2 )



From ( 1 ), length of 2nd side - length of 3rd side = 7cm ; So, x - y = 7 cm



Adding ( 1 ) & ( 2 ),



x + y = 13 cm

x - y = 7 cm
___________
2x = 20 cm
___________


x = $\dfrac{20\:cm}{2}$


x = 10 cm



Substituting the value of x in ( 2 )



x - y = 7 cm


10 cm - y = 7cm


10 cm - 7 cm = y


3 cm = y



Therefore, length of all sides of the triangle are : 9cm , 10cm , 3 cm



Now, finding area by Heron's formula,



semi perimeter ( s ) = $\dfrac{22}{2} cm$= 11 cm


applying Heron's formula :


area of the triangle = $\sqrt{11(11-10)(11-9)(11-3)} cm^{2}$


area of the triangle = $\sqrt{11(1)(2)(8)}$ cm²


area of the triangle = $\sqrt{176}$ cm²


area of the triangle = 4√11 cm²

$\:$

Answer 2

$\huge \bold {\mathfrak {hey}}$

$\huge \bold {See \: In \: Attachment}$

To find the area of triangle we can use Heron's formula

S = a +b +c /2
S = 9 + 10 + 3 / 2
S = 22 / 3
S = 11

Area of triangle =
$\sqrt{s(s - a)( s- b)(s - c)}$
_________________
/11( 11 - 9)(11 - 10)(11 - 3)

$\sqrt{11(2)(1)(8)}$
➡️ 11 × 2 × 2 × 2×2
➡️ ⬇️
$4 \sqrt{11}$

From above attachments and solutions we find the sides of triangle = 9cm, 10cm, 3cm and area of triangle = 4 root 11

Hope it will help you

Be Brainly

$\huge {Thank \: You}$