Question

Exercise 4 - the line (AC) is perpendicular to the line (AB) - the line (EB) is perpendicular to the line (AB) - the lines (AE) and (BC) intersect at D - AC = 2.4 cm; BD = 2.5 cm: DC = 1.5 cm Determine the area of triangle ABE.

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Hermann

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Identify the Right Angles:
AC is perpendicular to AB
EB is perpendicular to AB
This implies that triangle ABC is a right triangle.
Find Lengths:
AC = 2.4 cm
BD = 2.5 cm
DC = 1.5 cm
Use the Pythagorean Theorem in Triangle ABC:
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can find the length of AB.
AC^2 + BC^2 = AB^2
(2.4)^2 + (2.5)^2 = AB^2
5.76 + 6.25 = AB^2
12.01 = AB^2
AB ≈ sqrt(12.01)
AB ≈ 3.47 cm
Calculate the Area of Triangle ABE:
The area of a triangle is given by the formula:
Area = (1/2) * base * height
In this case, the base is AB and the height is DC.
Area = (1/2) * AB * DC
≈ (1/2) * 3.47 cm * 1.5 cm
≈ 2.60 square cm
The area of triangle ABE is approximately 2.60 square centimeters.

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