Question

the area of two similar triangle are 49 CM square and 64 CM respectively if the difference of the corresponding height is 10 cm then find the length of altitude in centimetre

Answer 1

The areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.
Let first triangle altitude be x then second one's is x+10
so, Area of first triangle/area of second triangle=altitude of first triangle/altitude of second triangle
so, 49/64=(x/x+10)²
so, (7/8)²=(x/x+10)²
so, 7/8=x/x+10
so, 7(x+10)=8x
so, 7x+70=8x
so, 7x-8x=-70
so, x=70
So, first triangle's altitude is 70 cm
and the second one's is 80 cm