Finding lenths of a rectangle?

Question

uhm if you have a rectangle with an area of 136cm squared and the perimeter of 50cm what are the dimensions of the rectangle

can you explain how you got the answer so ill know how to do it?

Answer 1

Let w equals the width of the rectangle

Let L represent the length

You come up with two equations as usual

wL=136---------->w=136/L

2(w+L)=50------>2w+2L=50

Sub first eqt into second

2(136/L)+2L=50

2L^2-50L+272=0

2(L^2-25L+136)=0

Factor the equation

2(L-8)(L-17)=0

L=8 cm or 17cm

We will get two answers the length could be 8 cm or 17 cm and the other is the width.  

Answer 2

Area=L*W

Perimeter=2L+2W

  2L+2W = 50   which is L+W=25 or L=25-W

  L*W=136   which is W*(25-W)=136

  

25W - W^2=136

W^2-25W+136=0

(W-17)(W-8) =0

W=17 with L=8 or W=8 with L=17...ANS

Answer 3

You have two sets of variables.  Solve for X in terms of Y then plug that into your second equation

X x Y = 136cmS

2X + 2Y = 50cm

X= 136/Y

2(136/y) + 2Y = 50

you can do the rest.

Answer 4

xy=136

2x+2y=50

x=136/y

2(136/y)+2y=50

272/y+2y=50

272+2y^2=50y

2(y^2-25y+136)=0

2(y-17)(y-8)=0

y=17 and 8

x=136/17 and x=136/8

x=8 and x=17

so the answers are 8 and 17

making the rectangle 8x17

make it a good day

Answer 5

Imagine a rectangle ABCD.

You know that AB x BC = 136cm^2 and that AB + BC = 25 cm.

So AB = 25 - BC --> (25 - BC) x BC = 136 --> BC^2 - 25BC + 136 = 0 that gives BC = 17 or 8. It is obvious that if you choose BC to be 17 cm, AB will be 8 and vice versa.

Answer 6

Relative values of a side (y):

xy = 136

y = 136/x

2(x + y) = 50

x + y = 25

y = 25 - x

Finding length of a side (x):

136/x = 25 - x

25x - x² = 136

x² - 25x = - 136

x² - 25/2x = - 136 + (- 25/2)²

x² - 25/2x = - 544/4 + 625/4

(x - 25/2)² =  81/4

x - 25/2 = 9/2

Length of a side:

x = 9/2 + 25/2

x = 34/2 or 17

Length of the other side:

= 136/17 or 8

Answer: 17 by 8 cm are the dimensions of the rectangle.

Proof (area is 136 square cm):

= 17 cm(8 cm)

= 136 cm

Proof (perimeter is 50 cm):

= 2(17 cm) + 2(8 cm)

= 34 cm + 16 cm

= 50 cm

Answer 7

The area can be found by multiplying the length and the width of a triangle.

l*w=136

The Perimeter is found by adding the lengths and the widths

l+l+w+w=50

Now you just have to do a little algebra with the two equations given.

2l+2w=50

l+w=25 (Divide by 2)

w=25-l

l*w=136

l*(25-l)=136

25l-l^2=136

l^2-25l+136=0

(l-8)(l-17)=0

So the length can either be 8 or 17, the width would just be the other one. (Ex. If you said the length was 8 the width would be 17)