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3 years ago

8

Factor 26r3s + 52r5 - 39r2s4

1 answer:

aniked [119]3 years ago

4 0

Hello,

26r^3s+52r^5-39r²s^4
=13r²(4r^3+2rs-3s^4)

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Please help!! MathsWatch, Surd Expressions, Clip 207c

dexar [7]

Answer:

$A=(72+36\sqrt{3})\ mm^2$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

Let

a ----> the height of rectangle in mm

b ---> the base of rectangle in mm

step 1

Find the base of rectangle

$b=AB+BC+CD+DE$ ----> by segment addition postulate

substitute

$b=3+3+3+3=12\ mm$

step 2

Find the height of rectangle

$a=FB+CG+GH$ ---> by segment addition postulate

substitute the given values

$a=3+CG+3\\a=6+CG$

Find the length sides CG

Applying the Pythagorean Theorem

$BG^2=BC^2+CG^2$

substitute the given values

$6^2=3^2+CG^2$

$CG^2=6^2-3^2$

$CG=\sqrt{27}\ mm$

simplify

$CG=3\sqrt{3}\ mm$

therefore

$a=(6+3\sqrt{3})\ mm$

step 3

Find the area of rectangle

$A=ab$

we have

$a=(6+3\sqrt{3})\ mm$

$b=12\ mm$

substitute

$A=(6+3\sqrt{3})(12)=(72+36\sqrt{3})\ mm^2$

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Step-by-step explanation:

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