SOLUTION: The triangle is isosceles and the perimeter equals 54 cm. The height is 3*sqrt(21). Find the lengths of the sides and the area of the triangle. Express your answers in simplest rad

Question 939227: The triangle is isosceles and the perimeter equals 54 cm. The height is 3*sqrt(21). Find the lengths of the sides and the area of the triangle. Express your answers in simplest radical form.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
definition of isosceles triangle: a triangle with two equal sides
---
the problem doesn't say which height is being talked about, so let's assume it's the height from the non-equal side (the base b), to the point where the two equal sides meet:
---
perimeter = 54 = 2s + b
2s = 54 - b
s = (54 - b)/2
---
length of the equal sides:
---
s = sqrt( hh + bb/4 )
(54 - b)/2 = sqrt( hh + bb/4 )
(54 - b)(54 - b)/4 = hh + bb/4
54*54 - 108b + bb = 4hh + bb
2916 - 108b = 4hh
108b = 2916 - 4hh
b = (2916 - 4hh)/108
b = (2916 - 4* 3*sqrt(21) * 3*sqrt(21) )/108
b = (2916 - 4*3*3*sqrt(21)*sqrt(21) )/108
b = (2916 - 4*3*3*21 )/108
b = 20 cm
s = (54 - b)/2
s = (54 - 20)/2
s = 17 cm
---
area:
---
a = bh/2
a = 20*3*sqrt(21)/2
a = 30*sqrt(21) sq.cm
---
Free algebra tutoring live chat:
https://sooeet.com/chat.php?gn=algebra
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations with quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
RELATED QUESTIONS
Give the measure of the base of an isosceles triangle whose perimeter is 60 cm and one of (answered by ikleyn)

An isosceles triangle is a triangle with two sides having the same measurement and one... (answered by Gogonati)

An isosceles triangle is a triangle with two sides having the same measurement and one... (answered by macston)

An isosceles triangle is a triangle with two sides having the same measurement and one... (answered by josgarithmetic)

The perimeter of a triangle is 36 cm and one of the legs is 3 cm larger than the other.... (answered by cleomenius)

The altitude (height) of an isosceles triangle is 3 cm and its perimeter is 18 cm. Find... (answered by richwmiller)

the perimeter of an isosceles triangle is 21 cm the length of each side is triple the... (answered by ewatrrr)

Find area of the isosceles triangle. Sides are sqrt of 11 and the base is... (answered by TimothyLamb)

One leg of an isosceles triangle has a length of (x2 + 9)cm. The base of the isosceles... (answered by solver91311)