Question

Each of the equal sides of an isosceles triangle is 2 cm more than its height and the base of the triange is 12 cm.find the area of triangle
​

Answer 1

Base = 12 cm,

Let the height be h cm

then,

equal sides = (h+2) cm

Area of the triangle =

2

1

×b×h

=

2

1

×12×h

=6hcm

2

...(i)

when equal sides are considered,

semi-perimeter =

2

(h+2)+(h+2)+12

=

2

2h+16

=(h+8)cm

By heron's formula,

Area =

S(S−a)(S−b)(S−c)

=

(h+8)(h+8−h−2)(h+8−h−2)(h+8−2)

=

(h+8)(6)(6)(h−4)

=

(h+8)(h−4)(36)

__ (ii)

Equating (i) and (ii), h = 8 cm

Area = 6h

=6×8 =48cm

2