Question

The base of triangle is of length b, and the altitude is of length h. A rectangle of height x is inscribed in the triangle with the base of the rectangle in the base of the triangle. The area of the rectangle is
​

Answer 1

Question:

The base of triangle is of length b, and the altitude is of length h. A rectangle of height x is inscribed in the triangle with the base of the rectangle in the base of the triangle. The area of the rectangle is

Answer:

bx

​

(h−x)

Step-by-step explanation:

△AOC∼△EGC [AA similarly]

∴  

EG

AO

​

=  

GC

OC

​

⇒  

x

h

​

=  

y

b/2

​

 

⇒y=  

2h

bx

​

⇒2y=  

h

bx

​

 

∴Base length of rectangle=b−2y

=b−  

h

bx

​

 

=b[1−  

h

x

​

]

∴Area of rectangle=x×b[1−  

h

x

​

]=  

h

bx(h−x)

​Conclusion:

It's complicated due to fractions.. but check the attached file for explanation :)