MATH SOLVE

6 months ago

Q:
# the length of a rectangular garden is 3 m greater than the width. The area of the garden is 70m squared. find the dimensions of the garden

Accepted Solution

A:

A = l x w

so you know that the length is 3m longer than the width, so you could use a formula to represent that

w = l + 3

you then substitute the second equation into the first to solve for l

70 = l x (l +3)

70 = l^2 + 3l

you could then rearrange the formula and solve for l using the quadratic formula

0 = l^2 + 3l - 70

l = -3 +- (square root (3)^2 - 4(1)(70)) / 2(1)

l = -3 +- (square root 9 + 280) / 2

l = -3 +- (square root 289) / 2

l = -3 +- 17 / 2

then you solve for the two seperate roots

l = -3 + 17 /2

l = 14 / 2

l = 7

or

l = -3 - 17 / 2

l = -20 / 2

l = -10

since a length cannot be negative, this root is not viable. therefore l = 7

to solve for w you would use

w = l + 3

w = 7 + 3

w = 10

hope this helps! if you did not understand a step or concept please let me know!

so you know that the length is 3m longer than the width, so you could use a formula to represent that

w = l + 3

you then substitute the second equation into the first to solve for l

70 = l x (l +3)

70 = l^2 + 3l

you could then rearrange the formula and solve for l using the quadratic formula

0 = l^2 + 3l - 70

l = -3 +- (square root (3)^2 - 4(1)(70)) / 2(1)

l = -3 +- (square root 9 + 280) / 2

l = -3 +- (square root 289) / 2

l = -3 +- 17 / 2

then you solve for the two seperate roots

l = -3 + 17 /2

l = 14 / 2

l = 7

or

l = -3 - 17 / 2

l = -20 / 2

l = -10

since a length cannot be negative, this root is not viable. therefore l = 7

to solve for w you would use

w = l + 3

w = 7 + 3

w = 10

hope this helps! if you did not understand a step or concept please let me know!