Question

if the difference between semi perimeter and sides of triangle ABC are 8 cm 7 cm and 5 cm respectively then find the area of the triangle

Answer 1

given, 

the difference between semi perimeter (s) and sides of a triangle are 8,7, and 5 
which means 

(s-a) =8 
(s-b) = 7
(s-c) = 5 

where a,b,c are the length of the sides of the triangle ABC 

area of triangle formula 

$\sqrt{s(s-a)(s-b)(s-c)}$

= $\sqrt{s(8)(7)(5)}$

= $\sqrt{s(280)}$

Answer 2

Answer:

The area of the triangle is 59 cm.

Step-by-step explanation:

The area of a triangle exists defined as the total region that is enclosed by the three sides of any separate triangle.

Given,

The perimeter and sides of triangle ABC are 8 cm 7 cm and 5 cm.

To find,

The area of the triangle.

Step 1

$\mathrm{s}-\mathrm{a}=8 \mathrm{~cm} \cdots(1)$

$s-b=7 c m \cdots(2)$

$\mathrm{s}-\mathrm{c}=5 \mathrm{~cm} \cdots(3)$

Where $a, b, c$ are the sides of the triangle.

$s_{2}$ is 1 semi perimeter ie $\mathrm{s}=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$

$(1) +(2)+(3)$

$\Rightarrow 3 \mathrm{~s}-(\mathrm{a}+\mathrm{b}+\mathrm{c})=20 \mathrm{~cm}$

$\Rightarrow 3 \mathrm{~s}-(25)=20 \mathrm{~cm}$

$\Rightarrow \mathrm{s}=20 \mathrm{~cm}$

Applying the equation,

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{20(8 \times 7 \times 5)$

$}=\sqrt{5600}=20 \sqrt{14$

$}=59 \mathrm{~cm}$.

#SPJ2