+0

# The length of a room is 1 more than 3 times its width. The area of the room is 80 square meters. Find the demensions.

0
321
7

The length of a room is 1 more than 3 times its width. The area of the room is 80 square meters. Find the demensions.

Guest May 8, 2015

### Best Answer

#4
+26416
+13

You are nearly right zacismyname.  However, you should take a closer look at your calculation of $$1^2-4\times3\times-80$$ under the square root sign.  It isn't 960 (almost, but not quite!).

You've nothing to be ashamed of!

.

Alan  May 8, 2015
Sort:

### 7+0 Answers

#1
+26416
+8

Let L be the length and W the width

L = 3W + 1                (1)   (I assume the room is 1 metre longer than 3 times the width)

L*W = 80                  (2)

Using (1) in (2)

(3W + 1)W = 80

Rearrange

3W2 + W - 80 = 0

This factors as

(3W + 16)(W - 5) = 0

Since we can't have a negative width for the room, the only valid solution is W = 5m

Using (1) this means that L = 3*5 + 1 = 16m

.

Alan  May 8, 2015
#2
+981
+5

The length of a room is 1 more than 3 times its width. The area of the room is 80 square meters. Find the demensions.

$$w\times{l}=A$$

$$w\times({3w+1})=80$$

$$3w^2+w=80$$

$$3w^2+w-80=0$$

$$w=\frac{-1+\sqrt{1^2-4\times{3}\times{-80}}}{2\times{3}}$$ or $$w=\frac{-1-\sqrt{1^2-4\times{3}\times{-80}}}{2\times{3}}$$

$$w=\frac{-1+\sqrt{961}}{6}$$ or $$w=\frac{-1-\sqrt{961}}{6}$$

$$w=\frac{{-1}+31}{6}$$

$$\mathbf{w=5}$$

$$l=3\times{5}+1}$$

$$\mathbf{l=16}$$

Fixed!

zacismyname  May 8, 2015
#3
+981
0

. . . I'm a bit ashamed I didn't see those factors

zacismyname  May 8, 2015
#4
+26416
+13
Best Answer

You are nearly right zacismyname.  However, you should take a closer look at your calculation of $$1^2-4\times3\times-80$$ under the square root sign.  It isn't 960 (almost, but not quite!).

You've nothing to be ashamed of!

.

Alan  May 8, 2015
#5
+981
+5

Bad choice of word I would have just preferred to factorise rather than use the formula.

zacismyname  May 8, 2015
#6
+91517
+5

You make a great contribution to this forum Zac :))

Melody  May 8, 2015
#7
+981
+5

Thanks :)

zacismyname  May 8, 2015

### 3 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details