Friday

February 27, 2015

February 27, 2015

Posted by **Mona** on Friday, February 1, 2013 at 12:12pm.

Thanks.

- Geometry-8th gr -
**Reiny**, Friday, February 1, 2013 at 2:24pmThis is a very tough question for grade 8, I am totally impressed.

make your sketch, let

AB = a

BC = b

BD = x

Angle B = 2Ø , so that angle ABD = Ø and angle BCD = Ø

I am going to use the fact that if we have triangle with sides a and b with Ø the angle between them

the area = (1/2)ab sinØ

area of triangle ABD= (1/2)ax sinØ

area of triangle BCD=(1/2)bx sinØ

But if we consider the bases along AC , the both have the same measured from B

so they are in the ratio of 15:21 or 5:7

then:

(1/2)axsinØ/( (1/2)bxsinØ ) = 5/7

canceling reduces this to

a/b = 5/7

5b = 7a

b = 7a/5 = 1.4a ---- ******

now let's use the perimeter:

a + b + 15+21 = 120

a+b =84 -----******

sub in b = 1.4a into the above equation

a+b = 84

a + 1.4a = 84

2.4a = 84**a = 84/2.4 = 35**

then b = 1.4(35) = 49

great question !!!!

- Geometry-8th gr -
**Steve**, Friday, February 1, 2013 at 3:31pmor, using the angle bisector theorem,

AD/DC = AB/BC

so, as Reiny calculated,

AB/BC = 5/7

AD+BC = 84

5x+12x=84

x=7

so, AB = 35

BC = 49

- Geometry-8th gr - typo -
**Steve**, Friday, February 1, 2013 at 3:32pmoops

5x+7x=84

x=7

- Geometry-8th gr -
**Mona**, Friday, February 1, 2013 at 5:21pmThanks.

**Answer this Question**

**Related Questions**

Geometry-8th gr - Find KN and LM. In triangle LKM, angle L is bisected. Line ...

Geometry - Find KN and LM. In triangle LKM, angle L is bisected. Line segment LK...

Geometry - Yes, I'm this desperate. I just have problems with coming up with the...

geometry - Given: M is the midpoint of line segment PQ and line segment RS. ...

geometry - Prove line segment BP is 2/3 of line segment BD in triangle ABC

Geometry - The perimeter of triangle ABC is 29 meters. Line segment AD bisects ...

geometry - A triangle is formed where line segment AC and line segment BC have ...

Geometry - Please write a paragraph proof for this statement. Point Y is the ...

Geometry - Please write a paragraph proof for this statement. 30: Point Y is ...

geometry - given: segment AB is paralell to segment DC; segment AB is congruent ...