Question

The difference of semi-perimeter and the sides of $\Delta ABC$ are $8cm,7cm$ and $5cm$, respectively. Its semi perimeter is:

• A. $10cm$
• B. $5cm$
• C. $15cm$
• D. $20cm$

Answer 1

The correct option is D $20cm$

Let $a,b,c$ are the measure of sides of $△ABC$

$S$ be the semi perimeter Then

$S-a=\mathrm{8..........}\left(1\right)S-b=\mathrm{7..........}\left(2\right)S-c=\mathrm{5...........}\left(3\right)$

Adding equation (1) (2) (3) we get

$3S-(a+b+c)=20S=\frac{a+b+c}{2}a+b+c=2s3s-2s=20s=20cm$