Question

Geometry question here!
Find the perimeter and area of each figure. Give your answers in simplest form.

17. a 45-45-90 (degrees, right isoceles) triangle with a hypontenuse length 12 in.

19. a square with diagonal length 18 meters

21. an equilateral triangle with height 30 yards



please help explain the steps to at least one of these pronlems. We are on chapter 5.8 of the Holt Geometry book.

Answer 1

17. An isosceles triangle is defined as having two equal sides. It's a right isosceles, so you know that the hypotenuse squared = one side squared plus the other side squared. Both sides are the same, so you get s^2 + s^2 = 144. Solve from there. The area of any right triangle is 1/2 base x height.

19. Same thing. The diagonal bisects the square into to right isosceles triangles.

21. Draw this one and bear in mind that all three sides are the same length (the definition of an equilateral triangle) and the height is a vertical line bisecting the triangle into two equal right triangles (not isosceles).

Answer 2

@ChristianGeek On 17, I got up until ' 2x^2 = 144 ' from there, it is invalid to say 2x^2 /2 = 144/2 , correct? Because that comes out as x^2 =72 , then 8.485... = 72 .. I'm so lost! Is there anyway you can explain how to work the equation so the answer comes out as x= instead of ' # = # ' ??

Answer 3

That's correct, the square root of 72 (which you can probably round to 8.5) is the length of each of the sides. Now you can figure out the perimeter: 8.5 + 8.5 + 12 and the area: 1/2 (8.5 x 8.5) or 1/2 (72).

I'm going offline for a couple of hours and may or may not be back later.

Answer 4

Alright. Thanks for all the help. @ChristianGeek