The perimeter of an isosceles triangle is 16cm. One of the sides equals to x+3, while the unequal one equals to x+4. Calculate the area of this triangle.
Firstly, we know that it is an isosceles triangle, meaning that 2 of its sides are equal. In this case, the uneven side is given as x+4, so we can assume that the triangle has 3 sides: AB= X+3BC= X+3AC= X+4The perimeter of a triangle is the sum of all its sides, therefore here we know that: Perimeter=AB+BC+AC 16=(x+3)+(x+3)+(x+4) 16= 3x+10 6=3x x=2SO: AB=5, BC=5, AC=6Area=(Base x Height )/2 = AC xAD/2Based on Pythagoras Theorem on the ADC triangle, AD2= AB2-AD2AD = AC/2 (as the triangle is isosceles) = 3so, AD2=25-9=16, AD=4AREA= 6 x 4/2= 12cm2
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