Question

ina triangle ABC angle B is equal to angle C
if BC=5and AB=4, then the perimeter of the triangle ABC formed by joining the midpoints off the sides triangle ABC is ​

Answer 1

$\huge\mathtt\pink{Answer}$

Given: A(x,y)≡(x

1

,y

1

),B(1,2)≡(x

2

,y

2

) and C(2,1)≡(x

3

,y

3

)

We know than area of triangle =

2

1

[x

1

(y

2

−y

3

)+x

2

((y

3

−y

1

))+x

3

(y

1

−y

2

)]

(hint: using determinant formula of the area of triangle)

Then area of triangle whoes vertex is A(x,y),B(1,2) and C(2,1) is

Area of ΔABC=[x(2−1)+1(1−y)+2(y−2)]=

2

1

(x+1−y+2y−4)=

2

1

(x+y−3)

But given that that the area of triangle is 6 sq unit

∴

2

1

(x+y−3)=6

⇒x+y−3=12

⇒x+y=15

Answer 2

Answer:

AB = 4 cm

Step-by-step explanation:

Given : In ΔABC

            ∠A=∠C

             BC=4 cm

              AC = 3 cm

To Find : AC

Solution :

Since   ∠A=∠C

So using property of triangle : opposite sides of equal angles are equal

⇒ BC=AB

Since BC= 4 cm

So, AB = 4 cm