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First I will check b = 6 cm:Īnd that's the same as 5 2, so it works. Because the hypotenuse if 27 cm, that means that the base and the height (the two remaining sides) will be equivalent. Both values of x are positive, therefore we have to carry two possibilities into this calculation: Given that is a 45/45/90 triangle, it means that its also isosceles. Which we can solve using "completing the square" method:īut recall that we want b, not x. Which is a quadratic in b^2 (this is just a formal way of saying a quadratic where the variable's value is a square of what we really want). Substitute this into the Pythagorean equation we wrote earlier: Now we can use the formula to find the area of the triangle: Area (1/2) x base x height. So get rid of the h by using the substitution method: So the height of the triangle is 3sqrt(3) cm. So you have two equations with two unknown values h and b (which you want to know). If you would like to learn more about the isosceles triangle, our isosceles triangle calculator is just the tool you need. You can also see the right triangles and notice that Pythagoras' Theorem must work here, so

Let b = the base of the isosceles triangle and h be its height. The area of a triangle is (1/2) base times height. This divides the triangle into two congruent right triangles, with that new line the height of the triangle.

The base of an isosceles triangle - Math Centralįind the base of an isosceles triangle whose area is 12sq.cm and the length of 1 of the equal sides is 5 cm.ĭraw the triangle with the shared vertex at the top and you can drop a bisector from that to the opposite side.