Question

# Find the area of an isosceles triangle whose one side is 10 cm greater than each of its equal sides and perimeter is 100 cm.

Hint:

### Let two equal sides be x cm

## The correct answer is: 200√5 cm2

### It is given that one side is 10 cm greater than each of its equal sides.

Let two equal sides be x cm

So, third side = x + 10

Perimeter = 100 cm.

i.e. Sum of all sides = 100

x + x + x + 10 = 100

3x = 90. ⇒ x = 30 cm

Two equal sides = 30 cm

Third side = 30 + 10 = 40 cm

Using Heron’s formula,

Area of triangle = where s =

s = = 50

Area of triangle =

=

=

=

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There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the

base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.

The figure above is the floor plan drawn by an architect for a small concert hall. The stage has depth 8 meters (m) and two walls each of

length 10 m. If the seating portion of the hall has an area of 180 square meters, what is the value of *x *?

**Note:**

There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the

base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.