Height and base

An isosceles triangle has an area of 168 cm2, and its added height and base are 50 cm. What are the measurements of its height and base?

Final Answer:

h =  42 cm
a =  8 cm

Step-by-step explanation:

S=168 cm2 s=50 cm h+a = s  S = 2a⋅ h​ S = 2(s−h)⋅ h​  S=(s−h)⋅ h/2  168=(50−h)⋅ h/2 0.5h2−25h+168=0  a=0.5;b=−25;c=168 D=b2−4ac=252−4⋅0.5⋅168=289 D>0  h1,2​=2a−b±D​​=125±289​​=25±171​ h1,2​=25±17 h1​=42 h2​=8  h=h1​=42=42 cm

Our quadratic equation calculator calculates it.

a=s−h=50−42=8=8 cm   Verifying Solution:   S1​=2a⋅ h​=28⋅ 42​=168 cm2 s2​=a+h=8+42=50 cm

Try calculation via our triangle calculator.


Try another example


Did you find an error or inaccuracy? Feel free to send us. Thank you!







Tips for related online calculators
Are you looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?
Calculation of an isosceles triangle.
Do you want to convert time units like minutes to seconds?
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

algebraplanimetricsUnits of physical quantitiesGrade of the word problem

 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: