In a rectangular trapezoid, the sides are 12cm and 13cm, and the large diagonal is 15cm.
| August 22, 2021 | education
In a rectangular trapezoid, the sides are 12cm and 13cm, and the large diagonal is 15cm. Find the bases of the trapezoid.
From the right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the leg AD.
AD ^ 2 = BD ^ 2 – AB ^ 2 = 152 – 122 = 225 – 144 = 81.
AD = 9 cm.
Let’s draw the height of the CH trapezoid. Since ABCH is a rectangle, the length of CH = AB = 12 cm.
In a right-angled triangle СDН, we define, according to the Pythagorean theorem, the length of the leg DH.
DH ^ 2 = CD ^ 2 – CH ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25.
DН = 5 cm.
The length of the segment АН = АD – DH = 9 – 5 = 4 cm.Then BC = АН = 4 cm.
Answer: The lengths of the bases of the trapezoid are 4 cm and 9 cm.
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