Question

The perimeter of an isosceles triangle is is 150cm and its unequal side is 70 cm find the area of the triangle

Answer 1

In an isosceles triangle, $<b>two sides are equal.</b>$



$<b>Step I :</b>$ $<u>Assumption</u>$

Let the First and Second sides be equal.

Also, First side = Second side = x cm




$<b>Step II :</b>$ $<u>Determine the magnitude of each equal side.</u>$

As we know,

Perimeter = Sum of all sides

Also, Perimeter = 150 cm ( Given )

$\therefore$

Sum of all sides = 150 cm

First Side + Second side + Third Side = 150

x + x + 70 = 150

2x = 150 - 70

2x = 80

x = 80 / 2

x = 40

First side = Second side = 40 cm




$<b>Step III :</b>$ $<u>Determine the area of triangle</u>$

$<I>By Heron's Formula</I>$

s = ( a + b + c ) / 2

Here, a, b & c are the sides.

s = ( 40 + 40 + 70 ) / 2

s = 150 / 2 = 75

Now,

Area of triangle = √ s ( s - a ) ( s - b ) ( s - c )

= √ 75 ( 75 - 40 ) ( 75 - 40 ) ( 75 - 70 )

= √ 75 * 35 * 35 * 5

= 5 * 5 * 7√15

= 175√15 cm²




Hence, $<u>the area of triangle is</u>$ $<b><u><I> 175√15 cm².</b></u></I>$