Question 17689
Express the Area A of an isoceles triangle with a height of 8 inches and a base of b inches as a function of the length s of one of its two equal sides
let the isocelles triangle be PQR with QR as base =b and equal sides PQ=PR=s,Let PS=h be the altitude from P to QR.since PQR is isocelles triangle QS=SR=b/2.further PQS is a right angled triangle.hence
PQ^2=QS^2+PS^2
s^2=(b/2)^2+h^2 or.s^2-h^2=b^2/4..or..b=Square root of [4(s^2-64)]
area =A = (1/2)*b*h=8*b/2=4b = 4*Square root of [4(s^2-64)]...........
A=8*Square root of [(s^2-64)]=