Hypotenuse AB of a right angled triangle ABC has been divided into four congruent segments by points G,E,H in the order A,G,E,H,B. if AB is equal to 20 cm find the squares of the measures from line segments from C to G,E and H
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The given question cannot be solved, as there is no Pythagorean triplet with 20 as the hypotenuse. So considering one of the sides as 20 cm, we get,
Given:
AB = 20 cm
To find:
If AB is equal to 20 cm find the squares of the measures from line segments from C to G,E and H
Solution:
Consider the attached figure while going through the following steps:
From given we have,
AB = 20 cm
AE = EB = AB/2 = 20/2 = 10 cm
AG = GE = AE/2 = 10/2 = 5 cm
EH = HB = EB/2 = 10/2 = 5 cm
According to Pythagorean triplets, we have,
20, 21, 29
Given, AB = 20 cm
⇒ AC = 21 cm
∴ BC = 29 cm
CG² = AC² + AG²
= 21² + 5²
= 466
∴ CG = 21.58 cm
CE² = AC² + AE²
= 21² + 10²
= 541
∴ CE = 23.25 cm
CH² = AC² + AH²
AH = AE + EH = 10 + 5 = 15
= 21² + 15²
= 666
∴ CH = 25.8 cm
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