Drawing Exercises

hey this one is sort of easy i got c is that right?

1.A rectangle is twice as long as it is wide. If both its dimensions are increased by 4 m, its area is increased by 88 m2. Make a sketch as in Oral Exercise 1. Find the dimensions of the original rectangle. A. 6 m wide, 12 m long B. 8 m wide, 16 m long C. 10 m wide, 20 m long D. 12 m wide, 24 m long

Public Comments

1. Let x = original short side, 2x = original long side. new short side = x +4, new long side = 2x + 4 Original Area = x * 2x = 2x^2 New Area = (2x+4)(x+4) = 2x^2 + 12x + 16 Original Area + 88 = New Area 2x^2 + 88 = 2x^2 + 12x +16 12x = 72 x = 6 A) 6m wide, 12 m long
2. (x+4)(2x+4)-2x^2=88 2x^2+12x+16-2x^2=88 12x+16=88 adding -16 12x=72 dividing by 12 x=6 so the dimensions of the original rectangle are 6m*12m
3. Original dimentions: l = 2*w Second area is 88 more than first area: (l + 4) * (w + 4) = l * w + 88 Mulitply it out: l*w + 4w + 4l + 16 = l*w + 88 Substitute 2w for every l and solve: 2w² + 12w + 16 = 2w² + 88 12w = 72 w = 6 l = 12 The answer is "a". Sorry.
4. x = original width 2x = original length 2x^2 = original area x+4 = new width 2x+4 = new length (x+4)(2x+4) = 2x^2 + 12x +16 = new area Thus 2x^2 +12x +16 - 2x^2 =88 12x +16 = 88 12x = 72 x = 6 = original width 2x = 12 =original length Sorry, the answer is A
5. A is the correct answer. 6 x 12 =72 72+ 88 =160 6 + 4 = 10 12 + 4 = 16 16 x 10 = 160