# Isosceles triangle

The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.

Result

z =  2.8 dm

#### Solution:

$r=5 \ \text{dm} \ \\ 20 \ cm=2 \ dm \ \\ \ \\ v=2 + z \ \\ r^2=v^2 + (z/2)^2 \ \\ \ \\ 5^2=(2+z)^2 + (z/2)^2 \ \\ \ \\ -1.25z^2 -4z +21=0 \ \\ 1.25z^2 +4z -21=0 \ \\ \ \\ a=1.25; b=4; c=-21 \ \\ D=b^2 - 4ac=4^2 - 4\cdot 1.25 \cdot (-21)=121 \ \\ D>0 \ \\ \ \\ z_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ -4 \pm \sqrt{ 121 } }{ 2.5 } \ \\ z_{1,2}=\dfrac{ -4 \pm 11 }{ 2.5 } \ \\ z_{1,2}=-1.6 \pm 4.4 \ \\ z_{1}=2.8 \ \\ z_{2}=-6 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 1.25 (z -2.8) (z +6)=0 \ \\ \ \\ z>0 \ \\ z=z_{1}=2.8=\dfrac{ 14 }{ 5 }=2.8 \ \text{dm} \ \\ v=2 + z=2 + 2.8=\dfrac{ 24 }{ 5 }=4.8 \ \text{dm} \ \\ r_{2}=\sqrt{ v^2 + (z/2)^2 }=\sqrt{ 4.8^2 + (2.8/2)^2 }=5 \ \text{dm}$

Checkout calculation with our calculator of quadratic equations.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. Right 24
Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
2. Triangle IRT
In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
3. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
4. Thunderstorm
The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tri
5. Catheti
The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
6. Median in right triangle
In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
7. Calculate
Calculate the length of a side of the equilateral triangle with an area of 50cm2.
8. RT and circles
Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
9. A truck
A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
10. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
11. Algebra
X+y=5, find xy (find the product of x and y if x+y = 5)