Mathematics: Asquare building with an area of 225 m2 has a garden surrounding it that has an equal width on all sides. the area of the garden is 1/3 of the area of the building. what is the width of the garden?

Asquare building with an area of 225 m2 has a garden

Ответ:

petroale000

15.01.2022

Mathematics

The width of the garden is 1.16 m

Step-by-step explanation:

step 1

Find the area of the garden

To find out the area of the garden multiply by 1/3 the area of the building

$225(\frac{1}{3})=75\ m^2$

step 2

Find the length side of the square building

The area of a square is

A=b^2

where

b is the length side of the square

we have

$A=225\ m^2$

$b^2=225\\b=15\ m$

step 3

Find the width of the garden

Let

x ----> the width of the garden

we know that

The area of the building plus the area of the garden is equal to

(15+2x)^2=225+75

solve for x

$225+60x+4x^2=225+75\\4x^2+60x-75=0$

Solve the quadratic equation by graphing

using a graphing tool

The solution is x=1.16 m

see the attached figure

therefore

The width of the garden is 1.16 m

Find the exact value

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

4x^2+60x-75=0

$a=4\\b=60\\c=-75$

substitute in the formula

$x=\frac{-60\pm\sqrt{60^{2}-4(4)(-75)}} {2(4)}$

$x=\frac{-60\pm\sqrt{4,800}} {8}$

$x=\frac{-60\pm40\sqrt{3}} {8}$

$x=\frac{-60+40\sqrt{3}} {8}\ m$ ----> exact value

Asquare building with an area of 225 m2 has a garden surrounding it that has an equal width on all s

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Ответ:

Justadumbemo

03.08.2021

Mathematics

let's say that point is point C, thus

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment}\\\\\\A(1,4)\qquad B(6,2)\qquad\qquad \stackrel{\textit{ratio from A to B}}{2:3}\\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(1,4)=2(6,2)\\\\[-0.35em]~\dotfill\\\\C=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em]~\dotfill$

$\bf C=\left(\cfrac{(3\cdot 1)+(2\cdot 6)}{2+3}\quad ,\quad \cfrac{(3\cdot 4)+(2\cdot 2)}{2+3}\right)\implies C=\left(\cfrac{3+12}{5}~,~\cfrac{12+4}{5} \right)\\\\\\C=\left( \cfrac{15}{5}~,~\cfrac{16}{5} \right)\implies C=\left( 3~,~3\frac{1}{5} \right)$

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Asquare building with an area of 225 m2 has a garden surrounding it that has an equal width on all sides. the area of the garden is 1/3 of the area of the building. what is the width of the garden?

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