Grade 12Differential Calculus

pic is attached ...please solve with diagram ...please

Question image for pic is attached ...please solve with diagram ...pl

milind

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below,

Arrangement is something like this, but in place of y, we have x & vice-versa.
Area of rectangle:
$xy$ …..........(1)
Area of triangle:
$\frac{1}{2}bh$ …........(2)
Now, we have three other portion remaining in the triangle other than rectangle. We are going to compare the area.
Area of bottom two triangles:
$\frac{1}{2}x.(b-y)$ ….....(3)
Area of upper triangle:
$\frac{1}{2}y.(h-x)$ ..........(4)

Now, we have
$(1) +(3)+(4) = (2)$
$xy + \frac{1}{2}y(h-x)+\frac{1}{2}x(b-y) = \frac{1}{2}bh$
$hy + bx = bh$
$y = \frac{b}{h}(h-x)$
Perimeter of rectangle:
$2(x+y)$
$2(x+b-\frac{b}{h}x)$
$2(b+(1-\frac{b}{h})x)$
Area of rectangle:
$xy$
$\frac{bx}{h}(h-x)$