SOLUTION: In the diagram equal angles are marked. Given that
EB=6 cm, CE 18 cm and DB=4 cm. Find the area of Triangle ABC.
https://ibb.co/vxJcWkc
Algebra.Com
Question 1209158: In the diagram equal angles are marked. Given that
EB=6 cm, CE 18 cm and DB=4 cm. Find the area of Triangle ABC.
https://ibb.co/vxJcWkc
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
In triangles ABC and EBD, we are given that angles BAC and BED are congruent. Then, since the two triangles share angle B, those two triangles are similar.
Corresponding sides BC and BD have lengths 24 and 4, so the ratio of similarity between the two triangles is 6:1.
The ratio of the areas of the two triangles is the square of the ratio of similarity, which is 36:1.
The diagram shows that angle EBD and EDB are congruent, so triangle EBD is isosceles. The altitude of triangle EDB from vertex E to side DB then cuts DB in half. From that, the Pythagorean Theorem tells us that that altitude of triangle EDB has length 4*sqrt(2); and from that we can find the area of triangle EDB is 8*sqrt(2).
And since the ratio of the areas of the two triangles is 36:1, the area of triangle ABC is 36*(8*sqrt(2)) = 288*sqrt(2).
ANSWER: 288*sqrt(2)
RELATED QUESTIONS
https://imgur.com/mlmAPzV In the diagram, angles marked are equal. BD = 4 cm and BC = 10... (answered by ikleyn)
In the diagram, AB = BC and BD=DC=CE. AB=4 cm. Find the length of AE, in cm.... (answered by ikleyn,math_tutor2020)
In the diagram, BD=15 cm and DC=6 cm. Find the ratio of the area of the parallelogram to... (answered by greenestamps)
In the diagram below, Triangle ABC is isosceles, and Triangle MPQ is equilateral. Find... (answered by ikleyn,Edwin McCravy)
In the diagram, ABCG is a parallelogram, and BF = 18 cm, FE = 6 cm. Find the length, in... (answered by greenestamps)
In the diagram to the right, Triangle ABC is isosceles, and Triangle MPQ is equilateral.... (answered by ikleyn)
In the diagram to the left, ∆ABC is isosceles, and ∆MPQ is equilateral.
Find the... (answered by MathLover1)
ABC is an equilateral triangle. DE and DF are perpendiculars drawn from D to the sides... (answered by ikleyn,MathTherapy)
In the diagram AD = 4 cm, EF = 3 cm, and parallel segments are indicated. If the total... (answered by math_tutor2020,ikleyn)