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3 years ago

The length of a rectangle is 3 feet more than 5 times its width. The perimeter of the rectangle is 42 feet.

Mathematics

1 answer:

poizon [28]3 years ago

6 0

42 = 2(W+L)

21= (W+L)

L= 3+5W)

21= W +(3+5W)

21= 3+6W

21-3=6W

18=6W

W=18/6

Answer:

w = PERIMETER/2 - LENGTH

w = 42/2 - (3+5w)

PS. I THINK THIS IS RIGHT. NOT TOO SURE, BUT MOST LIKELY.

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Step-by-step explanation:

Consider the below figure attached with this question.

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$base^2+perpendicular^2=hypotenuse^2$

Use Pythagoras in triangle HKL

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Taking square root on both sides.

$LH=12$

Let length of HI be x.

LI = 12+x

Use Pythagoras theorem in ΔKLI,

$(KI)^2+15^2=(12+x)^2$

$(KI)^2+225=x^2+24x+144$

$(KI)^2=x^2+24x+144-225$

$(KI)^2=x^2+24x-81...(1)$

Use Pythagoras theorem in ΔHKI,

$(KI)^2=x^2+9^2$

$(KI)^2=x^2+81...(2)$

From (1) and (2) we get

$x^2+81=x^2+24x-81$

$24x=162$

$x=\dfrac{162}{24}=6.75$

Hence, the measure of HI is 6.75 units.

Substitute x=6.75 in equation (2).

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$(KI)^2=126.5625$

Taking square root on both sides.

$KI=\sqrt{126.5625}$

$KI=11.25$

Hence, the measure of KI is 11.25 units.

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