SOLUTION: In the diagram, AB=2CB. The ratio of the area of the inscribed square to the area of triangle ABC is: A) 1:3 B) 2:5 C) 5:11 D) 4:7 E) 4:9 https://imageshack.com/i/poZ4rSWlj

SOLUTION: In the diagram, AB=2CB. The ratio of the area of the inscribed square to the area of triangle ABC is: A) 1:3 B) 2:5 C) 5:11 D) 4:7 E) 4:9 https://imageshack.com/i/poZ4rSWlj

Algebra.Com

Question 1167554: In the diagram, AB=2CB. The ratio of the area of the inscribed square to the area of triangle ABC is:
A) 1:3
B) 2:5
C) 5:11
D) 4:7
E) 4:9
https://imageshack.com/i/poZ4rSWlj
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let the measure of the sides of the square be

. Since triangles DFC and AED are formed by the sides of the square and must therefore be parallel to the sides of triangle ABC, triangles DFC and AED must be similar to ABC, and therefore their sides are in proportion.

So if CB is half of AB, then DE must be half of AE and CF must be half of DF. But since all four sides of the square are equal, CF is also half of CB and EB is half of AB.

So we have the area of the square as

, and then the long side of ABC is

and the short side is

, so the area is:

Then

John

My calculator said it, I believe it, that settles it

I > Ø

RELATED QUESTIONS
in the diagram AB = 2CB. the ratio of the area of the square to the area of triangle ABC... (answered by greenestamps)

A circle is inscribed in an equilateral triangle, and a square is inscribed in the... (answered by HasanSahin)

in the diagram, right triangle ABC is inscribed in circle O, angle ACB is a right angle,... (answered by cleomenius)

Triangle ABC below is isosceles, with AB=AC. A square is inscribed in the triangle, with... (answered by ikleyn)

Triangle ABC is isosceles, with Line AB=AC, and Line BC=39 cm A square is inscribed in... (answered by MathLover1)

A 5-12-13 triangle is inscribed in a circle, which is inscribed in a larger 5-12-13... (answered by ikleyn)

ABC is a triangle with sides a, b, and c, as shown in the diagram. If angle C = 90... (answered by Edwin McCravy)

In the diagram below, find the ratio of the area of the parallelogram to the area of... (answered by greenestamps)

The diameter of circle AOB is 12, Triangle ABC is inscribed in the circle, angle A = 45.... (answered by mangopeeler07,jim_thompson5910)