Question

The sum of the lengths of two sides of a triangle is 48 cm. If the perimeter of the triangle is 70 cm, then what is the difference between the semi-perimeter and the third side of the triangle?

• A.
  11 cm
• B.
  13 cm
• C.
  15 cm
• D.
  17 cm

Answer 1

The correct option is B

13 cm
Let the sides of the triangle be a, b and c.

Given that the sum of the lengths of two sides of the triangle is 48 cm.

$\therefore a+b=48cm\dots ..\left(i\right)\text{Also, given that the perimeter is 70 cm.}\therefore a+b+c=70cm\Rightarrow 48+c=70\left[From\right(i\left)\right]\Rightarrow c=70–48=22cm\therefore \text{Semi-perimeter of the triangle, (s)}=\frac{a+b+c}{2}=\frac{70}{2}=35cm$

Thus, the difference between the semi-perimeter and the third side $=35cm-22cm=13cm.$

Hence, the correct answer is option (b).