Find the area of the largest rectangle that can be inscribed in a right triangle with legs of length

Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 4 cm if two sides of the rectangle lie along the legs.

[AlexYoo-vx]

I missed few days of school and this is beyond helpful. Thanks for your video.

[leppaberry]

Would you need to adjust the calculations if the lengths of the sides were switched?

[OneManBackUp]

Love the simplicity. Keep up the good work :)

[armitagehux]

Thank I've been struggling with a similar question for ages now, and you've explained it in 5 minutes! Thank you so much

[shashwatbetala]

Hey I kinda noticed this a few times with this question. The max area of the rectangle always turns out to be exactly that of the total triangle... is that a thing or just like a recurring co-incidence

[allwanamar]

very clear and interesting . thank you

[Rupeshpamaihgari]

Hey one doubt!! Whats the reason behind assuming one of the sides of rectangle parallel to one side of triangle. Why cant we assume and how to derive same if one side of rectangle is parallel to hypotenuse of triangle ?

[fcar]

That f car  comment below was intended for the Norman Window problem.

[ptyptypty]

So, if x= 2.. then y = 1.5 ... since A = 3 = xy .... interesting to note that the x and y values are equal to ONE HALF of the length of their respective Legs of the I bet the dimensions of a Rectangle inside an ISOSCELES Triangle would be a Square.... but again with dimension of the square being 1/2 the values of the Triangle's Sides.. I wonder if there's a GENERAL FORMULA for the dimensions of a Rectangle in a Triangle that suggests .. Maximum Area of a Rectangle is Equal to One Half the Sides of the legs of the triangle.. ??... Great VIDEO!!..

[aafreenjahan]

I have a question that... Two sides of a triangle have length 12 m and 15 m. The angle between them is increasing at a rate of 2° / min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? Can u explain me this plsss...

[fcar]

It is a lot easier for students to learn the TECHNIQUE ..without getting into decimal type answers ..that waste time on math ..rather than procedure.