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The bisector of one of the angles of a rectangle also bisects a side of the rectangle. Find the perimeter of the rectangle if you know that the smaller side of the rectangle is equal to 10 cm.

Respuesta :

The answer is 60... Draw a rectangle. Now draw a line that splits the bottom left corner in two but also cuts the long side on the top in half. A rectangle has 4 right angles right? So the bisector, or a line that splits something in half, splits the right angle, a 90 degree angle, in half making it a 45 degree angle. Did you notice the bisector made a triangle?
A triangle has angle measures that always add up to 180 degrees. So you know that triangle has two angles: a 45 and 90 degree angle... Add those up and you get 135. 180-135 gives you the other angle: 45 degrees...
So you know that the triangle is a 45-45-90 triangle... The two legs or side lengths that I marked on the triangle with a small line are congruent in a 45-45-90 triangle and since the short leg of the rectangle is equal to 10cm and the split in half long side of the rectangle is also 10 which you double to 20. 20+20+10+10=60.
aksnkj

The perimeter of rectangle will be 60 cm.

Given,

The smaller side of rectangle is 10 cm.

Let the bigger side of rectangle be [tex]x[/tex] cm.

Since all angles measures 90 degrees in a rectangle so the bisector of one of the angle of rectangle bisects it into two equal angles of 45 degrees each.

As given in question,

The bisector of one of the angles of a rectangle also bisects a side of the rectangle( here bigger side ).

So if we take the triangle with the line joining the angle bisector to the opposite side then the base will be shorter side and the perpendicular will be half of bigger side.

Now consider the right triangle, by trigonometric ratios, we have

[tex]Tan\Theta=\dfrac{Perpendicular}{Base} \\[/tex]

[tex]Tan 45^{\circ}=\dfrac{\frac{x}{2} }{10}[/tex]

[tex]\dfrac{x}{2} =10\ (Tan45^{\circ}=1)[/tex]

[tex]x=20[/tex]

So bigger side will be 20 cm.

How to calculate the perimeter?

We know that the perimeter of rectangle is,

[tex]P=2(L+B)[/tex]

[tex]P=2(10+20)\\P=60 \ cm[/tex]

For more details about perimeter, follow the link:

https://brainly.com/question/897975

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