The given lengths of the sides of the isosceles triangle and the formed
right triangle are used to find the length of BC.
Reasons:
The given details of the isosceles triangle ΔABC are;
AB = AC = 4
AH = 3
Required:
To determine BC
Solution:
By Pythagorean theorem, we have;
[tex]\overline{BH}[/tex]² = 4² - 3² = 7
∴ [tex]\overline{BH}[/tex] = √7
Given that AH = 3, by segment addition property, we have;
AC = AH + HC
Which gives;
HC = AC - AH
HC = 4 - 3 = 1
By Pythagorean theorem, we have;
[tex]\overline{BC}^2[/tex] = [tex]\mathbf{\overline{BH}}[/tex]² + [tex]\mathbf{\overline{HC}}[/tex]²
Which gives;
[tex]\mathbf{\overline{BC}} = \sqrt{\overline{BH}^2 + \overline{HC}^2}[/tex]
BC = √((√7)² + 1²) = √(8)
Learn more about Pythagorean theorem here:
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