The length and width of a rectangle are in the ration 5:3.. perimeter is 32 cm. Find length and width. Write an equation to solve it. Thank you.
- print Print
- list Cite
Expert Answers
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Let the length be "L" and the width "W"
We know that the ration is 5:3
Then, L/W = 5/3
Cross multiply:
==> 3L = 5W
==> L = (5/3)*W .......(1)
Also, it is given that the perimeter P is 32:
==> 2L + 2W = 32 .......(2)
Now substitute (1) in (2):
==> 2 (5/3)W + 2W = 32
==> (10/3)W + 2W = 32
==> (16/3)W = 32
Multiply by 3/16:
==> W = 32*3/16 = 6
==> W = 6 cm.
==> L = (5/3)w = (5/3)*6 = 10
==> L = 10 cm
Related Questions
- Find the length and width of a rectangle whose perimeter is equal to 160 cm and its length is...
- 2 Educator Answers
- The width of a rectangle is 9 cm less than twice the length. The perimeter is 72 cm. What is the...
- 1 Educator Answer
- The length of a rectangle is 5 inches more than its width. If the perimeter of the rectangle is...
- 1 Educator Answer
- The length l of a rectangle is decreasing at the rate of 2 cm/sec while the width w is increasing...
- 1 Educator Answer
- The length of a rectangle is twice its width. If the perimeter is 36 ft find its area.
- 2 Educator Answers
Given :
perimeter = 32
2[length + breadth] = 32
length + breadth = 16
---------------------------------------------------------
Sun of ratio = 5+3 = 8
length = 5/8 * 16 = 10 cm
breadth = 3/8 * 16 = 6 cm
Given that ratio of length and width is 5:3.
Length/Width = 5/3
==> Width = Length*(3/5)
Perimeter of a rectangle = 2*(Length + Width) = 32 cm (Given)
Substituting value of width as Length*(3/5) in above equation of perimeter:
2*(Length + Length*3/5) = 32
==> (16/5)*Length = 32
Therefore:
Length = 5*32/16 = 10 cm
Given ratio of length to width is 5:3
Therefore:
Width = Length*(3/5) = 10*3/5 = 6 cm
Answer:
Length = 10 cm
Width = 6 cm
length and width are in the ratio 3:5 , the perimeter = 32.
Since perimeter is 2 times lthe sum of length and breadth, the sum of the lenth and breadth = 32cm/2 = 16cm.
Now 16 cm could be divided into 5:3 ratio by:
{5/(5+3)}16cm and {3/(5+3)}16cm or
(5*16/8) cm and (3*16/8)cm or
5*2 cm and 3*2cm
10 cm and 6 cm.
Therefore the length and breadth of the rectangle are 10cm and 6cm..
Check: the ratio of length and breadth 10cm : 6cm . Divide the two terms by 2cm and the ratio is 10cm/2cm : 6cm/2cm . Or 5:3.
P = 2(length+breadth) = 2(10+6) = 32.
Student Answers