Question

The rectangle above consists of five congruent rectangles, the longer side of each being x m. If the total area of the figure is 7500 m2, what will be the value of x ?​

Answer 1

Answer:

The perimeter of the original rectangle is 165. So the combined length and the width add up to 165/2 or 82.5.

One rectangle can be 42.5 x 40. The 5 congruent smaller rectangles will be 42.5x8. The perimeter of each will be (42.5+8)*2 = 101.

The next rectangle can be 47.5 x 35. The 5 congruent smaller rectangles will be 47.5x7. The perimeter of each will be (47.5+7)*2 = 109.

The next rectangle can be 52.5 x 30. The 5 congruent smaller rectangles will be 52.5x6. The perimeter of each will be (52.5+6)*2 = 117.

The next rectangle can be 57.5 x 25. The 5 congruent smaller rectangles will be 57.5x5. The perimeter of each will be (57.5+5)*2 = 125.

The next rectangle can be 62.5 x 20. The 5 congruent smaller rectangles will be 62.5x4. The perimeter of each will be (62.5+4)*2 = 133.

The next rectangle can be 67.5 x 15. The 5 congruent smaller rectangles will be 67.5x3. The perimeter of each will be (67.5+3)*2 = 141.

The next rectangle can be 72.5 x 10. The 5 congruent smaller rectangles will be 72.5x2. The perimeter of each will be (72.5+2)*2 = 149.

The next rectangle can be 52.5 x 30. The 5 congruent smaller rectangles will be 77.5x1. The perimeter of each will be (77.5+1)*2 = 157.

Since the statement says that there are 5 congruent rectangles making up a single rectangle (of perimeter 165 units)

I would assume following to be the image of the question above:

So due to this,

14x = 165 units

Therefore, x = (165/14)

So perimeter of any one of small rectangle is (Since all small rectangles are congruent)

2x + 2x + x + x = 70.71 units

Therefore, perimeter of small rectangle = 70.71 units

Fig 1:

•••••••• x = 2y

|———————————————|

| ………| ………| ………| ………| ………|

y| ………| ………| ………| ………| ………|

|—w—|—w—|—w—|—w—|—w—|

Solution:

Let

Width of main rectangle = y

Assuming length of rectangle =x= 2y

Perimeter of Big rectangle = y+y+x+x

y+y+2y+2y = 165

6y = 165

y = 165/6 = 27.5

Then x = 2y = 2×27.5 = 55

Now x = 55

y = 27.5

Let the x= 55 units is equally divided into 5 pieces of 11 unit length.

Let it be =w= 11 unit

Then perimeter of one small rectangle

= y+y+w+w = 27.5 + 27.5 + 11 +11 = 77

Checking:

2×(w+w+w+w+w) + y + y

= 2×(11+11+11+11+11)+27.5+27.5

=2×55+55=110+55=165 unit

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