arif's backyard is 22 by 32 meters. he wants to put a flower garden in the middle of the backyard, leaving a strip of grass of uniform width around the flower garden. to be happy, arif must have 288 m^2 of grass. under these conditions what will the length and width of the garden be?

Question

14-10-2022
Mathematics

Answered

arif's backyard is 22 by 32 meters. he wants to put a flower garden in the middle of the backyard, leaving a strip of grass of uniform width around the flower garden. to be happy, arif must have 288 m^2 of grass. under these conditions what will the length and width of the garden be?

Answer :

Other Questions

I NEED HELP PLS!!!! Reese is installing an in-ground rectangular pool in her backyard. Her pool will be 30 feet long, 14 feet wide, and have an average depth of

The coordinates of points a and b are a(2, 16) and b(22, 4). what are the coordinates of the point that is 34 of the way from a to b?

The graph of f(x) = 7x is stretched vertically by a factor of five. Which of the following is the equation of the new graph, g(x)? A. g(x) = 5(7x) B. g(x) = 7(5

The scores for assessments are displayed in the box-and-whiskers plot below. What is the range of the middle 50% of the data of scores on the assignment?

Select the correct values. if the area (in square units) of the region under the curve of the function f(x) = 3x − 1 on the interval [a, 4], where a < 4, is

The scores for assessments are displayed in the box-and-whiskers plot below. What is the range of the middle 50% of the data of scores on the assessment?

Select all of the true statements. A. π is the area of a circle of radius 1 B. π is the area of diameter 1 C. π is the circumfrence of a circle of radius 1 D. π

A ship sails 40 nautical miles (nm) due west from point A and then changes course and sails 20 nautical miles in a direction that is 54° west of due north. A di

Let the graph of g be a translation 2 units right followed by a horizontal shrink by a factor oft of the graph of f(x) = x^2 + x. Write a rule g.

ayune ayune · Answer 1 · 2022-10-18T09:22:20-04:00

The dimension of the flower garden, which located in the middle of the backyard surrounded by a strip of grass, is 26 m length and 16 m width.

The situation can be depicted on the attached picture.

We need to translate the word problem into algebraic expressions.

Let x be the width of the grass strip.

Let A be the area of the grass strip.

Then,

A = 2 . 22x + 2 . (32 - 2x)x

288 = 2 . 22x + 2 . (32 - 2x)x (divide by 2)

144 = 22x + x(32 - 2x) (divide by 2)

72 = 11x + x(16 - x)

72 = 27x - x²

x² - 27x + 72 = 0

This is a quadratic equation. One of the methods to solve a quadratic equation is by factorization.

Factorize the left side:

(x - 3) (x - 24) = 0

x = 3 or x = 24

The length of the flower garden = 32 - 2x

The width of the flower garden = 22 - 2x

Substitute x = 3:

The length of the flower garden = 32 - 2 . 3 = 32 - 6 = 26 m

The width of the flower garden = 22 - 2 . 3 = 16 m

Note that if we substitute x = 24, it will results in negative values while the dimension is always positive.

Learn more about quadratic equations here:

https://brainly.com/question/27849764

#SPJ4

​arif's backyard is 22 by 32 meters. he wants to put a flower garden in the middle of the​ backyard, leaving a strip of grass of uniform width around the flower garden. to be​ happy, arif must have 288 m^2 of grass. under these conditions what will the length and width of the garden​ be?

Answer :

Other Questions

arif's backyard is 22 by 32 meters. he wants to put a flower garden in the middle of the backyard, leaving a strip of grass of uniform width around the flower garden. to be happy, arif must have 288 m^2 of grass. under these conditions what will the length and width of the garden be?