Verified answer

Area of triangle= 1/2 base x height

So, height= area divide 1/2 base

height= 60/12 =5

Assuming the congruent sides areee equal use Pythagerian Theorem to find one side's length:

12squared + 5squared= Xsquared

144 + 25 = 169

sq. root of 169 is 13.

Therefore each of the other sides measure 13.

To determine the lengths of the congruent sides of the

Given the area (a)60 and the base (b)24 you can use the formula for the area of a triangle to determine the triangles height (h).

a = 1/2 b x h

transpose the formula so you can determine the height.

h = a / (1/2 b)

Now enter your variables.

h = 60 / (1/2 x 24)

h = 60 / (12)

h = 5

Now you can calculate the length of the congruent sides. By bisecting your isosceles triangle you can create a right angle triangle and use pythagorean theorem to solve the length of the congruent sides.

a^2 + b^2 = c^2

a and b being the sides that we know the length of and c being the hypotenuse of the right angle triangle.

a = height of the triangle

b = base of the triangle (remember to create a right angle triangle we folded it in half (bisected) so it is half of the original base dimension)

c = length of hypotenuse

5^2 x 12^2 = c^2

25 + 144 = c^2

169 = c^2

13 = c (the square root of 169 is 13.

Therefore the length of the congruent sides is 13.

Well, an isosceles triangle's sides can be found with some trigonometry.

First, let's find the height of this isosceles triangle.

You probably know that Triangular Area= (1/2)(base)(height)

So knowing that Area=60 and Base =24, Substitute to get...

60= (1/2)(24)(height)

60=12(height)

5=height

Now you have a right triangle on each half of the isosceles triangle.

Each half of the isosceles triangle has 1/2 base height, height, and the hypotenuse

Knowing that a^2+b^2=c^2, you can solve for the hypotenuse!

(1/2 base height)^2 + (height)^2 = (hypotenuse)^2

((1/2)24)^2 + (5)^2 = (hypotenuse)^2

(12)^2+25 = (hypotenuse)^2

(12)^2+25 = (hypotenuse)^2

144+25 = (hypotenuse)^2

169 = (hypotenuse)^2

13 = hypotenuse

I know that's long, but hopefully writing it out gives more of an explanation for you.

I hope that helps! :)

Find the altitude from the base (2*60/24)

Find half the base (24/2).

Now, each congruent half of the triangle forms a right-angled triangle with sides the altitude and one half of the base around the right angle, and hypotenuse one of the equal sides. So then the square of the equal sides is the sum of the square of the altitude and of the half of the base, and the side is the square root of this.

Drop a perpendicujar height to the base , it bisects the base , now first find the height= 2*60/24 =5 , use theorem pythagogras to find the congruent sides= sqrt(12^2+5^2)=13

Area= 1/2 base x height

60 = 0.5 * 24 * height

height = 5

Now consider two right-angled triangles each with base 12 and height 5

This is a standard 5,12,13 triangle so hypotenuse is 13.