the area of an isosceles triangle land whose base side length is 10m is 60 m^2. Find the measure of its remaining sides
Answers
We are given:
units of measurement are meters (m).
an isosceles triangle
base = 10 m
area = 60 m^2
To find the measure, I believe means find the equal sides or perhaps the isosceles triangle’s perimeter.
What do we know related to a base and area of a triangle.
A = 1/2 bh or 60 = 1/2(10)h => 60 = 5h and h = 12 m
Therefore, the altitude or height = 12m.
The altitude bisects the base. It is, in fact, a perpendicular bisector forming 2 right triangles whose hypotenuse is the side of the isosceles triangle.
Lets call the 2 equal sides “s”. Therefore,
h^2 + (b/2)^2 = s^2 substitute and solve for s.
12^2 + (10/2)^2 = s^2
144 + 25 = s^2
169 = s^2 => s = +/- 13. Only +13 will be used because a side length is positive.
Thus, the measure of the sides of the isosceles triangles Is: base = 10m, and sides = 13m
The perimeter is: 10m + 26m = 36 m
Answer: 36 m