Lena K. answered • 07/11/19

Private Math Tutor

Since this is a right triangle, we know we have to use the Pythagorean Theorem: **A**^{2}** + B**^{2}** = C**^{2}** , **where A and B = the legs of the triangle (which are shorter than the hypotenuse) and C = the hypotenuse.

In this isosceles triangle, A = B (because the legs are the same size) and C is 10cm longer than A and B.

Thus we get the following,

A = x

B = x

C = x + 10

We simply plug in these variables into the equation and solve for x:

x^{2} + x^{2} = (x+10)^{2}

2x^{2} = x^{2} + 20x + 100

x^{2 }- 20x - 100 = 0

We solve for x by completing the square:

(x^{2} - 20x + 100) - 100 = 100

(x-10)^{2} -100 = 100

(x-10)^{2} = 200

x - 10 = √(200)

x - 10 = 10 √2

x = 10 + 10√2 = 24

Finally,

**A ≈ 24** (or 10 + 10√2)

**B ≈ 24** (or 10 + 10√2)

**C ≈ 24** + 10 ≈ 34 (or 10 + 10√2 + 10 = 20 + 10√2)