Question

Gabriella wants to tile a room with an area of 320 square feet. The width of the room is 4/5 its length. What are the length and width of the room?

Answer 1

Read below.

Explanation:

A=l*w

320=l*(4/5)l

320=(4/5)(l2)

(5/4)(320)=(5/4)(4/5)(l2)

5(80)=l2 (320/4=80)

400=l2

√400=√l2

20=l

w=(4/5)(20)

w=4*4 (20/5=4)

w=16

length=20 feet

width=16 feet

If you don't understand square roots, maybe you understand prime factorization.

320=2*2*2*2*2*2*5=(2*2*2*2)*(2*2*5)=16*20 and 16 is 4/5 of 20

If you don't understand prime factorization you can use trial and error.

2*160

4*80

5*64

8*40

10*32

16*20 answer, because 16 is 4/5 or 0.8 times 20

Answer 2

lenght - a
width - b
Area= a*b
320=ab
b=4/5a
320=
`4a^(2)/5`
400=
`a^(2)`
a=
`√(400)`
a=20
b=16