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Agnishom

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From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

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Perimeter of Trapezium

The parallel sides of a trapezium are 3 cm and 9 cm. The non-parallel  sides are 4 cm and 6 cm. A line paralel to the bases divides the trapezium of equal perimeters. The ratio of the non-parallel sides  in which they are  divided  is what?

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Bob

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Registered: 2010-06-20

Posts: 10,621

Re: Perimeter of Trapezium

hi Agnishom

Diagram below.

If FG, DE and BC are all parallel, then by similar shapes

Let x, y, and z be as shown.

Then equal perimeters means

The 'z's cancel so you can simplify this to an equation in x and y.

and

In this the xy terms will cancel leading to a second equation in x and y.

Can you complete this by solving the simultaneous equations?

Bob

Last edited by Bob (2011-12-03 07:27:20)

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Perimeter of Trapezium

hi Haileypeelpost

Thanks for the nice comment.

Welcome to the forum. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gyanshrestha

Member

Registered: 2007-11-06

Posts: 41

Re: Perimeter of Trapezium

interesting answer. Here i find that the non parallel sides are divided into 1:3 ratio.

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anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Perimeter of Trapezium

hi gyanshrestha

how'd you get that?

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