If the equal sides are s and the base is b,
2s+b = 50
(b/2)^2 + 5^2 = s^2
For QRST, TQS is an isosceles right triangle, so QS = 8√2
QRS is isosceles, with vertex angle 60°, so QR=RS=√8 = 2√2. So, QRS is equilateral.
So diagonal TR is the sum of the two altitudes of the isosceles triangles:
4√6+4√2 = 4(√6+√2)
1. The perimeter of an isosceles triangle is 50cm and the length of the altitude to the base is 5cm. Find the length of the base.
2. In quadrilateral QRST:
TQ=8cm; (angle)R=60; (angle)T=90; QR=RS; ST=8cm.
Find the exact length of the longer diagonal of the quadrilateral.
1 answer