Question

A rectangle's length and width are in a ratio of 5:2. The area is 160 square centimeters. What are the length and width?

If you could solve this please do so asap

Answer 1

length = 20 cm and width = 8 cm

Explanation:

l - length

w - width

length and width are in a ratio of 5:2

`(l)/(w)=(5)/(2)` cross multiply

`2l=5w` divide both sides by 2

`l=(5w)/(2)`

the area is 160cm²

`lw=160`

We have the system of equations:

`\left\{\begin{array}{ccc}l=(5w)/(2)&(1)\\lw=160&(2)\end{array}\right`

Substitute (1) to (2):

`\left((5w)/(2)\right)(w)=160\\\\(5w^2)/(2)=160\qquad\text{multiply both sides by 2}\\\\5w^2=320\qquad\text{divide both sides by 5}\\\\w^2=64\to w=√(64)\\\\w=8`

Put the value of w to (1):

`l=((5)(8))/(2)=(40)/(2)=20`

Answer 2

Answer: The length and width are 20 square centimeters and 8 square centimeters

Explain: 20:8 can be reduced to 5:2 as a ratio. 20 times 8 equals 160.