Question

in a right angled triangle ABC, if ∆B = 90° AB-BC=2cm;AC-BC = 4 its perimeter is 24 cm find the area of triangle​

Answer 1

Hello,

Here we go,

Given : let ABC be a right angle triangle at Angle B

AB-BC = 2cm................1

AC-BC = 4cm................2

Perimeter of triangle is 24cm

AB + BC + AC = 24

(2+ BC) + BC + (4+ BC) = 24 ........................from 1 and 2

6 + 3BC = 24

3BC = 24-6

BC = 18/3=6cm

So,

AB = 2+BC=2+6=8cm

AC = 10 cm

Now ,

Area of triangle ABC

1/2 x base x height

1/2xABxBC

1/2x8x6

24cm²

I hope my answer will help you.

Answer 2

Answer:-

Given Angle B = 90° , (AB-BC)=2cm, (AC-BC)=4cm And perimeter = 24cm

Area of ∆ABC = (1/2)×AB×BC

Perimeter of ∆ABC= AB+BC+AC

(AB+BC+AC)= 24

AB= (24-BC-AC)

Given (AB-BC)=2

put value of AB here

(24-BC-AC)-BC= 2

24-2BC-AC= 2

AC= (24-2BC-2)

Also Given (AC-BC)=4cm

Now, put value of AC here

(24-2BC-2)-BC= 4

(22-3BC)=4

-3BC= 4-22

-3BC= -18

★BC= 6cm

Now put value of BC here ( AC-BC)=4

(AC-6)= 4

AC=4+6

★AC = 10cm

Put value of BC here ( AB-BC)=2cm

(AB-6)=2

★AB=8cm

Therefore Area of ∆ABC= (1/2)×8×6

Area of ∆ABC=24cm²

♥Wow! this was such an interesting Question.

This Triangle has perimeter and area same..osm!!