The length and breadth of a rectangular field are in the ratio 3:2. If the area of the field is 294 square metres, what is the cost of fencing the field at 28 per metre?
Answer is Rs. 1960
The ratio of the length of a rectangle to its width is 4:3. Its area is 300 square inches. What are its length and width?
Let the length is 4 x and breadth is 3 x4 x * 3 x=300 square inches12x^2 =300x^2 =25x =5 inchesLength = 4*5=20breadth=3*5=15 inches
If the side of a square is tripled, how many times will its area be as compared to the area of the original square?
The area would be 9 times compared to the area of the original square. To test this, you can let the side of the original square be equal 1. By tripling this side, the side becomes three. Utilizing the area of a square formula, A= s^2, the area of the original square would be 1 after substituting 1 for s. Then, you do the same for the area of the tripled square. With the substitution, the area of the tripled square would be 9. This result displays the area of the tripled square being 9 times as large as the area of the original square. This pattern can be used for other measurements of the square such as:let s = 2, Original Area= 2^2 = 4 Tripled Area= (2(3))^2 = 6^2= 36. 36/4 = 9let s = 3, Original Area = 3^2 = 9 Tripled Area - (3(3))^2 = 9^2 =81. 81/9 = 9let s = 4, Original Area = 4^2 = 16 Tripled Area - (4(3))^2 = 12^2 = 144. 144/16 = 9let s = 5, Original Area = 5^2 = 25 Tripled Area - (5(3))^2 = 15^2 = 225. 225/25 = 9let s = 6, Original Area = 6^2 = 36 Tripled Area - (6(3))^2 = 18^2 = 324. 324/36 = 9let s = 7, Original Area = 7^2 = 49 Tripled Area - (7(3))^2 = 21^2 = 2,401. 2,401/49 = 9You can continue to increase the length of the square and follow this pattern and it will be consistent.
The length of the sides of a square are multiplied by 3.5. How is the ratio of the areas related to the ratio of the sides?
area₁ = s² area₂ = (3.5s)² = 3.5²s² = 12.25s² ratio of area₂ to area₁ = 12.25:1 ===== Just realized that I misread the question. The ratio of the areas is the square of the ratio of the sides.
If ratio of length and breadth of a rectangle is 3:2 & its area is 38400 then find its perimeter?
Let the length be [math]l[/math] and breadth be [math]b[/math]. Therefore, as per the given condition [math]\frac{l}{b}=\frac{3}{2}[/math].[math]\therefore l=\frac{3b}{2}[/math]Let the area of rectangle be [math]A[/math] which is given as [math]38400 units^{2}[/math][math]\therefore A=l×b[/math][math]\therefore 38400=\frac{3b}{2}×b[/math][math]\therefore \frac{38400×2}{3}=b^2[/math][math]\therefore 25600=b^2[/math]Taking square roots,[math]\therefore b=160[/math] units.Putting value of b in l, we get,[math]\therefore l=\frac{3×160}{2}[/math][math]\therefore l=240[/math] units.Let the perimeter be [math]P[/math]. Hence, [math]P=2(l+b)[/math][math]\therefore P=2(240+160)=800[/math] units.Hence, perimeter of the rectangle is 800 units.Hope this helps! You can also get such questions solved and get the detailed solution within seconds using the Scholr app by just uploading a picture of the question and also get to be a part of an ever-growing community of students.
The length and breadth of a rectangle are in the ratio 3:2. The perimeter is 100 cm, find its area?
Perimeter of rectangle = 100mratio of length is to breadth = 3:2 = 3x : 2xPerimeter = 2(l+b)P = 2(3x+2x)= 6x + 4x = 10x10x = 100 ; x = 100/10 = 10l = 3x = 3 × 10 = 30 mb = 2x = 2 × 10 = 20 mArea of rectangle = length × breadth ( l×b )A = 30 × 20 = 600 sq.m
What is the relationship between area and volume?
Imagine a cube 1 foot on a side (substitute “meter” for “foot” if you like). Its volume will be 1 cubic foot. Each side is one square foot, so its total surface area is 6 square feet (because the cube has 6 sides).Now imagine a cube 3 feet on a side. Its volume will be 27 cubic feet (3 × 3 × 3). Each side is 9 square feet (3 feet by 3 feet), so its total surface area is 54 square feet.What has happened? The linear dimensions are 3 times bigger. The surface area has increased 9 times (54 ÷ 6). But the volume has increased 27 times (27 ÷ 1).Let's calculate surface area to volume ratios:For the 1-foot cube, 6:1.For the 3-foot cube, 54:27, or 2:1.For a 10-foot cube, 600:1000, or 0.6:1.As the cube gets bigger, the volume increases much more rapidly than the surface area, because the volume increases as the cube of the linear dimension, but the surface area increases as the square. This relationship applies, not just to cubes, but to spheres and any other fixed shape.
What is the answer if square is inscribed in the circle then the ratio of there area will give what?
Let side of square be 'a'Area of square is a²Diagonal of sqare is √{a²+a²}Or √2aSo diameter of circle is equal to diagonal of sqare.Then diameter=√2aRadius(r)=√2a/2=a/√2Area of circle=πr²=π{a/√2}²=πa²/2Ratio of area of square and area of circle =a²:πa²/2=1:π/2=2:π
A square board has an inscribed circle with a 15in radius. A small button is dropped 10,000 times on the board?
The probability of landing in the circle is (area of the circle)/ (area of the square) = (pi* r^2)/s^2 Since the radius of the inscribed circle is 15, the side of the square will be 30. So an estimate is 7852/10000=( pi*15^2) /(30^2) .7852 = pi* (1/2)^2 .7852* 4= pi 3.1408 = pi This is a close estimate of pi. I hope this helps!
Find Ratio: A picture in an art museum is 6 feet wide and 8 feet long..........?
It's E. 8ft x 12" =96" long. 6ft x 12" =72" wide. Area of actual painting is 96 x 72 = 6912 square inches. Area of frame is: 2 times (96x6) + 2 times [(72+12)6] = 1152 + 1008=2160 square inches 2160/6912=.3125 and 5/16=.3125 2160: 6912 = 5:16 It's E. I hope it helps.