Triangle ABC below has a right angle C and a height CD. (A height in a triangle connects its vertex and the opposite side, and i

Question

1 month ago

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s perpendicular to that side.) d If AC is 3 units long and BC is 4 units long, what is the length of CD?

1 answer:

zzz [12.3K] · Answer 1 · 2026-03-04T17:56:04+03:00

Answer:

2.4 units

Step-by-step explanation:

The area of triangle calculations apply to this problem.

Area of triangle = 1/3(base * height)

where it's given that

AC = 3 units

BC = 4 units

To determine the hypotenuse, we use the formula = $\sqrt{a^2 + b^2}$

where a and b represent the two legs of the right triangle, excluding the hypotenuse.

This leads to hypotenuse(AB) = $\sqrt{3^2 + 4^2} = \sqrt{25} = 5$

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The area of the triangle with a base of 3 units (AC) and a height of 4 units (BC) is calculated as

= 1/3(4 * 3) = 4 square units.

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Now consider another height, CD,

which is the perpendicular from point C to line AB.

If CD acts as height, the corresponding base will be the line on which this perpendicular is extended.

In this case, it's side AB, which is the hypotenuse with a calculated length of 5 units.

Recalculating the area of the same triangle using height CD and base AB,

we can express the area of triangle ABC as 1/3(CD * AB) = 1/3(CD * 5) ------------equation A

Given that the area of triangle ABC is 4 square units,

1/3(CD * 5) = 4 square units.

Consequently, CD = (4 * 3)/5 = 12/5 = 2.4 units.

Thus, length of CD = 2.4 units.