A square of the side lenght of 6cm has the same area as this rectangle . find the perimeter of the rectangle.

Mathematics

1 answer:

Aleksandr-060686 [28]1 year ago

3 0

Answer:

The perimeter of the rectangle is 26 cm

Step-by-step explanation:

First find the area of the square by multiplying 6 by itself

A = 6 cm * 6 cm = 36 sq cm

Since the rectangle has the same area as the square, we can say that w * 9 = 36 sq cm

w * 9 = 36

Divide both sides by 9 to isolate the variable, w

w * 9 / 9 = 36 / 9

w = 4 cm

The width of the rectangle is 4 cm so now we just use that to find the perimeter of the rectangle

P = 2(9) + 2(4) = 26 cm

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The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points $(-4,\ -1)$ and $\left(\dfrac{1}{2},\ 3\right)$ .

Substitute:

$m=\dfrac{3-(-1)}{\frac{1}{2}-(-4)}=\dfrac{4}{4\frac{1}{2}}=\dfrac{4}{\frac{9}{2}}=4\cdot\dfrac{2}{9}=\dfrac{8}{9}\\\\y-(-1)=\dfrac{8}{9}(x-(-4))\\\\y+1=\dfrac{8}{9}(x+4)$

The standard form: Ax + By = C

$y+1=\dfrac{8}{9}(x+4)\qquad\text{multiply both sides by 9}\\\\9y+9=8(x+4)\qquad\text{use distributive property}\\\\9y+9=8x+32\qquad\text{subtract 9 from both sides}\\\\9y=8x+23\qquad\text{subtract 8x from both sides}\\\\-8x+9y=23\qquad\text{change the signs}\\\\\boxed{8x-9y=23}$