The area of a rectangle gets reduced

Let the length and the breadth of the rectangle be x m and y m, respectively. ∴ Area of the rectangle = (xy) sq.m Case 1: When the length is reduced by 5m and the breadth is increased by 3 m: New length = (x – 5) m New breadth = (y + 3) m ∴ New area = (x – 5) (y + 3) sq.m ∴ xy – (x – 5) (y + 3) = 8 ⇒ xy – [xy – 5y + 3x – 15] = 8 ⇒ xy – xy + 5y – 3x + 15 = 8 ⇒ 3x – 5y = 7………(i) Case 2: When the length is increased by 3 m and the breadth is increased by 2 m: New length = (x + 3) m New breadth = (y + 2) m ∴ New area = (x + 3) (y + 2) sq.m ⇒ (x + 3) (y + 2) – xy = 74 ⇒ [xy + 3y + 2x + 6] – xy = 74 ⇒ 2x + 3y = 68………(ii) On multiplying (i) by 3 and (ii) by 5, we get: 9x – 15y = 21……….(iii) 10x + 15y = 340………(iv) On adding (iii) and (iv), we get: 19x = 361 ⇒ x = 19 On substituting x = 19 in (iii), we get: 9 × 19 – 15y = 21 ⇒171 – 15y = 21 ⇒15y = (171 – 21) = 150 ⇒y = 10 Hence, the length is 19m and the breadth is 10m.

You multiply the area by the scale factor twice. Here is an example: if we have a rectangle that has a length 3 and a height of 4 and the scale drawing with a scale factor of 2, how many times bigger is the scale drawings area? The original shape is 3 by 4 so we multiply those to find the area of 12 square units. The new shape has length of 3x2 (3 x the scale factor) and height of 4x2 (4 x the scale factor). The dimensions of our scale drawing are 6 by 8 which gives us an area of 48 square units. Notice when we found the new dimensions we multiplied the 3 and 4 EACH by the scale factor. So the new area could be found 3 x 4 x scale factor x scale factor. 48/12 = 4 which is the scale factor times the scale factor with a scale factor of 3 3x4 = 12 units squared 9x12 = 108 units squared 3x4x3x3 = 108 units squared 108/12 = 9 (scale factor x scale factor) The same concept applies to any two-dimensional shape. For example, if you had a triangle with a base measuring 6 units, and a height measuring 3 units, the area would be 9 square units. If we scale it by 1/3, the triangle's base is 2 units, the height is 1 unit, and the area is 1 square unit. The dimensions were scaled by 1/3, but the area was scaled by 1/9 (1/3 * 1/3). Hope this helps! You may not be able to "prove" it for all figures, but you could for regular polygons which you could find the area of, or you could break down a polygon into simpler figures of triangles and quadrilaterals that you could find the area of, and...

Q 1. Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be". (Isn't this interesting?) Represent this situation algebraically and graphically. SOLUTION: Soln. : At present : Let Aftab's age = x years His daughter's age = y years Seven years ago : Aftab's age = ( x - 7)years Daughter's age = ( y - 7)years According to the condition, [Aftab's age] = 7[His daughter's age] ⇒ [ x - 7] = 7[ y - 7] ⇒ x - 7 = 7 y - 49 ⇒ x - 7 y -7 + 49 = 0 ⇒ x - 7 y + 42 = 0 ..... (1) After three years : Aftab's age = ( x + 3) years His daughter's age = ( y + 3) years According to the condition, [Aftab's age] = 3[His daughter's age] ⇒ [ x + 3] = 3[ y + 3] ⇒ x + 3 = 3 y + 9 ⇒ x - 3 y + 3 - 9 = 0 ⇒ x - 3 y - 6 = 0 .... (2) Graphical representation of equation (1) and (2) : From equation (1), we have : From equation (2), we have The lines l 1 and l 2 intersect at (42, 12). Q 2. The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically. SOLUTION: Soln. : Let the cost of a bat = ₹ x and the cost of a ball = ₹ y ∴ Cost of 3 bats = ₹ 3 x and Cost of 6 balls = ₹ 6 y Again, cost of 1 bat = ₹ x and Cost of 3 balls = ₹ 3 y Algebraic representation : Cost of 3 bats + Cost of 6 balls = ₹ 3900 ⇒ 3 x + 6 y = 3900 ⇒ x + 2 y = 1300 ..... (1) Also, cost of 1 bat + cost of 3 ba...

Quick navigation: • • • • Area of a rectangle formula The formula for the area of a rectangle is width x height, as seen in the figure below: All you need are two measurements and you can calculate its perimeter by hand, or by using our perimeter of a rectangle calculator above. The result will be in the unit the width and height are measured in, but squared, e.g. mm 2, cm 2, m 2, km 2 or in 2, ft 2, yd 2, mi 2. How to calculate the area of a rectangle? The calculation is straightforward using the formula above: just make sure you have the measurement of the width and height in the same units, and then multiply them. Don't forget to express the result in the squared unit, and you are good to go. Example: find the area of a rectangle The area of any rectangular place is or surface is its length multiplied by its width. For example, a garden shaped as a rectangle with a length of 10 yards and width of 3 yards has an area of 10 x 3 = 30 square yards. A rectangular bedroom with one wall being 15 feet long and the other being 12 feet long is simply 12 x 15 = 180 square feet. Since in multiplication the order in which the numbers are multiplied does not matter, you need not worry about switching the places of the two measurements. Practical applications Area of a rectangle calculations have a vast array of practical applications: construction, landscaping, internal decoration, architecture, engineering, physics, and so on and so forth. Irregularly shaped areas are often divided ...