The bases of an isosceles trapezoid are 4 and 14, the side is 13. Find the length of the diagonal of the trapezoid.

univerkov | March 31, 2021 | education

Let’s draw the heights of Bh1 and Ch2,

Segment h1h2 = BC = 4,

And the segments Ah1 = Dh2 = (AD – h1h2): 2 = (14 – 4): 2 = 5,

Ah1 = 5,

Now, by the Pythagorean theorem, we find the side of Ch2,

Bh2 = 12,

Let’s find the side of Ah2,

Ah2 = Ah1 = h1h2 = 5 = 4 = 9,

Ah2 = 9,

Now we find the diagonal AC,

Answer: AC = 15.

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