Question

a rectangle is 3 times as long as it is wide. if length is increased by 6 and the width by 8, the area is increased by 108cm. what are the original dimensions

Answer 1

@Directrix

Answer 2

@hartnn

Answer 3

do you know the formula of area of rectangle ?

Answer 4

l times with

Answer 5

yes, let length = l and width = w
rectangle is 3 times as long as it is wide. ----> l=3w
got this ?

Answer 6

yes ok

Answer 7

length is increased by 6 ----> l+6
width by 8,------>w+8
so, what will be the new area ?

Answer 8

lwtimes86 48 so lw48

Answer 9

?

Answer 10

help

Answer 11

hello

Answer 12

sorry for late reply, i was away.
it would be product of length and width ,right ?
so, whats (l+6)(w+8)=...?
also, you know that, l=3w

Answer 13

lw+8l+6w+48=108

Answer 14

Since the area of a rectangle is Length x Width, and the area of the new triangle with increased dimensions 108, and we know that one side is 3x + 6 (The length) and the other side side is x + 8 (The width), then the area must be:

A = L x W
108 = (3x + 6) * (x + 8)
108 = 3x^2 + 30x + 48

Now bring 108 on to other side to form a single quadratic then factor the quadratic to get the values of x:

3x^2 + 30x - 60 = 0

Since this quadratic can't be factored normally, we use the quadratic formula. Using the quadratic formula we get the values x = -11.7082, 1.7082

Obviously, since x represents length, and length is always positive, then the correct value of x must be approximately 1.7082. Therefore x = 1.7082.

Now since we know the dimensions of our original rectangle were length = 3x and width = x, we just plug in 1.7082 for x to get the side lengths:

Length = 3x = 3*(1.7082) = 5.1246
Width = x = 1.7082