My mother is working in a high school and she is helping students that need extra help. They had a math problem that my mother just knew that I could solve. I can't so I am here. We know that the answer is B. We just don't know why. Thank you for all your help.
The sides of a rectangle are in the ratio 5:7 and the perimeter of the rectangle is 96 cm. What is the area of the rectangle?
a. 980 cm2 c. 462 cm2
b. 560 cm2 d. 418 cm2
2007-12-03 07:30:30 · 8 answers · asked by onefootnaked 4 in Science & Mathematics ➔ Mathematics
Since the ratio is 5:7, we can set the sides of the rectangle to 5x by 7x, so:
5x + 5x + 7x + 7x = 96
24x = 96
x = 4
So the rectangle is 5x by 7x and x = 4, meaning the rectangle is 20 by 28.
The area would be 20*28 = 560
Hope this helps! :) Best of luck!
2007-12-03 07:36:47 · answer #1 · answered by disposable_hero_too 6 · 1⤊ 1⤋
From the formula for perimeter of a rectangle:
P = 2L+ 2W -> 96=LW
Then from the problem, the ratio between the sides are 5:7.
W:L=5:7 -> L/W=5/7 -> 7W=5L -> W = (5/7)L
Then substitute:
96 = 2L + 2(5/7)L
96 = 2L + 10L/7
96 = 24L/7
24L = 672
L = 28cm
Then plug in L to the perimeter equation:
96 = 56 + 2W
W = 20cm
Then A = LW = 20*28 = 560cm^2
2007-12-03 15:42:22 · answer #2 · answered by someone2841 3 · 0⤊ 1⤋
5 + 7 = 12
96 div 12 = 8
8 x 5 = 40
8 x 7 = 56
40 div 2 = 20
56 div 2 = 28
20x 28 = 560 B
2007-12-03 15:43:54 · answer #3 · answered by ViewtifulJoe 4 · 0⤊ 1⤋
Let l be the length and w the width.
Then l/w = 5/7
So l = 5w/7.
Also 2l + 2w = 96
l + w = 48
5w/7 + w = 48
12w = 48*7
w = 4*7 = 28
l = 5*28/7 = 20
Area = lw = 28*20 = 560.
Hope that helps all of you!
2007-12-03 15:39:34 · answer #4 · answered by steiner1745 7 · 0⤊ 1⤋
Ratio 5:7, perimeter 96cm. Two sides of 5 and two sides of 7 give you perimeter of 24. You need 4 times that, or sides of 20 and 28 to add to perimeter total and keep ratio 5:7 (20:28). Thus the area is base * height, 20cm*28cm=560cm^2.
2007-12-03 15:38:15 · answer #5 · answered by Goethe's Ghostwriter 7 · 0⤊ 2⤋
Let width be 5x, length be 7x.
Then perimeter = 2(5x + 7x) = 96
24x = 96
x = 4
Width = 5x = 20
Length = 7x = 28
Area = L X W = 20 X 28 = 560
My compliments to your mother and you.
2007-12-03 15:42:32 · answer #6 · answered by Joe L 5 · 1⤊ 0⤋
2h + 2b = 96
2(20) + 2(28) = 96
Therefore, the height and the base are 20cm and 28cm
20 x 28 = 560cm2
2007-12-03 15:39:36 · answer #7 · answered by ohyeah 3 · 0⤊ 1⤋
So you're getting help to help your mom that helps students?
2(5x + 7x) = perimeter
24x = perimeter
perimeter = 96cm
24x = 96cm
x = 4cm
Sides are 5x and 7x
20cm * 28cm = 560cm^2
2007-12-03 15:36:56 · answer #8 · answered by UnknownD 6 · 0⤊ 1⤋