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- agha79
- Students
- Posts: 3
- Joined: Mon Aug 29, 2011 3:57 am
OG Page 260 Problem 8 and 9
i have no idea how to draw pictures so please can someone walk me through question 8 and 9 at page 260 of official guide?
- tommywallach
- Manhattan Prep Staff
- Posts: 1917
- Joined: Thu Mar 31, 2011 11:18 am
Re: OG Page 260 Problem 8 and 9
Hey Agha,
The easiest way to think about Question #9 is that the hypotenuse is increasing by a factor of 3 when moving from the smallest triangle to the largest triangle, meaning both the base and the height of the triangle are increasing by a factor of 3 (the large triangle and the small triangle are similar, because they share angle D and a right angle, so their third angle must be equal as well).
So the original area a * b = 42, must become 3a * 3b = x, or 9ab = x. 9 * 42 = 378.
Another way you could do it is to drop heights down from point C and from point B. If you do this, you'll see that the triangle is going to divide into 9 separate triangles the exact same size as CDE (the original small triangle).
Make sense?
-t
The easiest way to think about Question #9 is that the hypotenuse is increasing by a factor of 3 when moving from the smallest triangle to the largest triangle, meaning both the base and the height of the triangle are increasing by a factor of 3 (the large triangle and the small triangle are similar, because they share angle D and a right angle, so their third angle must be equal as well).
So the original area a * b = 42, must become 3a * 3b = x, or 9ab = x. 9 * 42 = 378.
Another way you could do it is to drop heights down from point C and from point B. If you do this, you'll see that the triangle is going to divide into 9 separate triangles the exact same size as CDE (the original small triangle).
Make sense?
-t
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