Apool measuring 10 feet by 20 feet will have a cement walkway around it. the area covered by the pool and the cement walkway is 600 square feet. if the walkway must have a uniform width around the entire pool, what is the width of the walkway?

the width of the walkway is 5 feet

Step-by-step explanation:

Let x represent the width of the walkway.

If the walkway must have a uniform width around the entire pool, it means that

The width of the total area would be x + 10 + x = 10 + 2x

The length of the total area would be x + 20 + x = 20 + 2x

The area covered by the pool and the cement walkway is 600 square feet. This means that

(10 + 2x)(20 + 2x) = 600

200 + 20x + 40x + 4x^2 = 600

4x^2 + 60x + 200 - 600 = 0

4x^2 + 60x - 400 = 0

Dividing through by 4, it becomes

x^2 + 15x - 100 = 0

x^2 + 20x - 5x - 100 = 0

x(x + 20) - 5(x + 20) = 0

(x + 20)(x - 5) = 0

x = 5 or x = - 20

Since the width cannot be negative, then, the width of the walkway would be 5 feet on all sides.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

so, converting firstly the mixed fractions to improper fractions and then "adding".