Question
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.
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.
Answers
Steve
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)
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)