5 Identical Rectangles

Looking at the picture you can see that the length of each small rectangle is $\frac{30}{2} = 15$ , and the height is $\frac{30}{3} = 10$ . And the height of the figure, then is $15+10 = \boxed{25}$

Let a be the width and b be the height of a small rectangle. Notices that 2b = 30 and 3a =30. By solving the those two equation, we get a=15 and b=10; thus, the height of the big rectangle is 25.

top level w=30/2=15 bott. l l=30/3=10 so 15+10=25 uint

Let the height of the figure be y. Also let the breadth of each rectangle be x. Then,area of the figure=l×b=30y _(i)

Area of each rectangle included=15x Then,Area of the five rectangle included in the figure=5×15x=75x _(ii)

From (i) and (ii) 30y=75x y=75x/30 (iii)

Also, y=15+x _(iv)

75x/30=15+x

By solving this equation,we get x=10

Putting value of x in equation (iv) then,y=25

Hence the height of the figure = 25

Dimensions of each small rectangle: l = 15, w = x

Area of a small rectangle = 15x

Area of the whole figure calculated as the sum of the areas of the small rectangles = 5(15x) = 75x

Area of the whole figure calculated directly = 30 * (15 + x) = 450 + 30x

Setting the two expressions for the area of the whole figure equal to each other and solving for x:

75x = 450 + 30x

x = 10

Therefore width (W) of the whole figure = 15 + 10 = 25