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Draw a line joining the top vertex to the middle of the base.

This divides the triangle into two right-angled triangles, which are congruent (both have the same side lengths and angles).

Each right-angled triangle has a hypotenuse length of 34 cm (the hypotenuse is the side opposite the right angle). They also have a side which is the height of the triangle, 30 cm.

By Pythagoras' theorem, the third side of each right-angled triangle is 16 cm long

because 342 - 302 = 1156 - 900 = 256 = 162

The base of the isosceles triangle is twice that, so it's 32 cm long.

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Q: What is the base length of an isosceles triangle that two sides are 34 cm and the height is 30?
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