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

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.

Answer 2

Answer:

length = 20 cm and width = 8 cm

Step-by-step explanation:

l - length

w - width

length and width are in a ratio of 5:2

$\dfrac{l}{w}=\dfrac{5}{2}$           cross multiply

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

$l=\dfrac{5w}{2}$

the area is 160cm²

$lw=160$

We have the system of equations:

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

Substitute (1) to (2):

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

Put the value of w to (1):

$l=\dfrac{(5)(8)}{2}=\dfrac{40}{2}=20$