MHB Length of a side, possible triangle side

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The discussion focuses on solving a problem involving an isosceles triangle from a mathematics for machine technology book. To determine the lengths of sides A and B, it's crucial to recognize the triangle's isosceles nature. Side A can be calculated by adding 7 inches to half of the base, while side B requires finding the height of the triangle using the Pythagorean theorem. The height is derived from the formula involving the triangle's dimensions, leading to the calculation of side B. The thread emphasizes the importance of understanding triangle properties and applying relevant mathematical principles to solve the problem.
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Tsroll said:
I have one question from my mathematics for machine technology book that has me stumped as well as my Father in-law, sister in-law and my accountant friend.

I wasn't sure if I was supposed to create a right triangle and use A² + B² = C²

Problem 18. B

http://s182.photobucket.com/user/da...1-499C-AF27-9DE175F5EF68_zps7ltszocb.jpg.html

First of all, you have to notice that the triangle is isosceles. This is important as the calculations wouldn't work out otherwise.

To find A, you need to add 7 inches to HALF of the base of the triangle.

To find B, you need to find the height of the triangle (if you draw in the height you will create two right-angle triangles, and you can use Pythagoras). Once you have the height of the triangle, subtract it from 17.823 inches.
 
As the triangle is isosceles I believe $A=7+0.5\times 30.263$

and $B=17.823 - h$ where $h$ is the height of the triangle. Have a go at finding it.
 
17.823 - √[(18.09)² - (30.263/2)²] = 7.909
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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