Math Is Fun Forum

Gerry

Member

Registered: 2006-06-10

Posts: 1

Calculate unknown length of split triangle - URGENT !!!

Hi,

I have got a triangle split into a triangle and a trapezium. All side lengths (left 4cm, right 4.8cm) and base (5cm) of the triangle are given. The left side of the trapezium is 6cm which makes the left side of the big triangle 10cm.

The information given is:
BE is parallel to CD. ABC and AED are straight lines. AB=4cm,BC=6cm,BE=5cm,AE=4.8cm.

Question:
Calculate the length of CD.
Calculate the length of ED.

I have been trying to solve this for the last few hours and am completely stuck. If someone could give advice or formula on how to solve this, it would be much appreciated. Answer not necessarily required - only looking for the formula.

Thanks in advance.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Calculate unknown length of split triangle - URGENT !!!

I am trying to visualize the problem (a sketch would be good!)

I *think* you have two Similar triangles (have a read of that link): ACD is the large one and ABE is the small one, and they have the angle A in common. Tell me if I am wrong.

If so, then ABE has all lengths known, and you can "scale" it to find the lengths of the bigger ACD.

The length AB is 4, and the length BC is 6, so a known side of the larger triangle AC is 4+6=10, and the ratio of the two sides is 10/4.

Therefore the side CD should be (10/4) * 5 = 12.5, and the side AD should be (10/4)*4.8 = 12, so ED = 12-4.8 = 7.2

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman