Question

ABC is a triangle….right angled at B.If AB=20cm.and BC= 21cm, find AC?​

Answer 1

Step-by-step explanation:

Answer:

6 units

Step-by-step explanation:

Given,

The sides of the triangle ABC,

AB =20cm , BC=21cm, AC =29cm,

Thus, the semi perimeter of the triangle ABC,

s=\frac{1}{2}(AB+BC + AC)=\frac{1}{2}(20+21+29)=\frac{1}{2}(70)=35s=

2

1

(AB+BC+AC)=

2

1

(20+21+29)=

2

1

(70)=35

So, by the heron's formula,

The area of the triangle,

A=\sqrt{s(s-AB)(s-BC)(s-AC)}A=

s(s−AB)(s−BC)(s−AC)

=\sqrt{35(35-20)(35-21)(35-29)}=

35(35−20)(35−21)(35−29)

=\sqrt{35(15)(14)(6)}=

35(15)(14)(6)

= 210 square unit,

Hence, the radius of the circle touching all the sides of triangle ABC,

R=\frac{A}{s}=\frac{210}{35}=6\text{ unit}R=

s

A

=

35

210

=6 unit

Answer 2

ANSWER :- 29CM

SOLUTION:-

(AC)²=(AB)²+(BC)²

(AC)²=(20)²+(21)²

(AC)²=400+441

(AC)²=841

AC=√841

AC=√29×29

AC=29 CM

HENCE,THE ANSWER IS 29 CM.