Question

In the isosceles triangle ABC, we have AB=AC=4. The altitude from B meets AC at H. If AH=3(HC) then determine BC.

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

The given lengths of the sides of the isosceles triangle and the formed

right triangle are used to find the length of BC.

• BC is √(8) units

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;

$\overline{BH}$² = 4² - 3² = 7

∴ $\overline{BH}$ = √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;

$\overline{BC}^2$ = $\mathbf{\overline{BH}}$² + $\mathbf{\overline{HC}}$²

Which gives;

$\mathbf{\overline{BC}} = \sqrt{\overline{BH}^2 + \overline{HC}^2}$

BC = √((√7)² + 1²) = √(8)

• BC = √(8)

Learn more about Pythagorean theorem here:

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