Question

A right triangle has legs 4 cm and 3cm. How far from the vertex must this triangle be cut by a line parallel to the longer diagonal so that:

(a) the area of the small right triangle will be equal to the area of the trapezoid formed

(b) the perimeter of the small triangle is equal to the perimeter of the trapezoid

Answer 1

I'm guessing we'll have to find the measure of CO

Answer 2

for part a) we need find where E, D such that area EDC = area ABDE
Suppose we have it, that is area EDC = area ABDE but sum of them = area ABC = 6
hence 2 area EDC = 6, area EDC =3
but area EDC = 1/2(EC*DC)=3 --> EC*DC=6 (*)
Now, \(\triangle ECD \eqsim \triangle ACB\), we have \(\dfrac{EC}{ED}=\dfrac{AC}{AB}=\dfrac{3}{4}\implies EC=(3/4) ED(**)\)
from(*)(**), we can find EC, ED. I let you finish the stuff.

Answer 3

part b is easy, right? just perimeters. Apply exactly method from part a

Answer 4

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