PS : Triangle

Question

ps

FN · Answer

the triangle is a 3:4:5 where the x factor is 5..

so height is 20 and base=15, which leaves area to b e 1/2*15*20 or 150

amitdgr · Answer

That was fast !! But I did not understand

1) how do we know triangle is 3:4:5 2) x factor is 5 ( what is x factor how did you get it as 5 ?) isn't the base supposed to be 16+9 = 25 ?

FN · Answer

you should memorize the famous right triangles they are 3:4:5, 5:12:13 etc

in this case it was obvious that hyp is 25 which is a multiple of 5..so i knew the x factor is 5..

3:4:5
15:20:25

LiveStronger · Answer

D - 150 fresinha12: Can you please explain your method :roll:

I went by the traditional way of 3 traingles(PQS, QSR, PQR), 3 variables(PQ, QS, QR), 3 equations Area = 1/2 * 25 * QS After solving the 3 equations you will get QS = 12, So area = 150 But, I would rather solve it with faster approach :wink:

GMAT TIGER · Answer

But where in the question it is mentioned that the sides of the traingle PQR are in the ratio of 3:4:5?

I also got 150 but differently: 
QS = x
PQ = a
QR = b

a^2 = 16^2 + x^2
b^2 = 9^2 + x^2

25^2 = a^2 + b^2
25^2 = 16^2 + x^2 + 9^2 + x^2
625 = 2x^2 + 337
x = 12

So a = 20 and b = 15

area = 1/2 (20x15) = 150

amitdgr · Answer

Ahh!! Good ol' Pythagoras ..... Thanks GMAT TIGER... +1!

spiridon · Answer

there are several shorcuts to calculate sides for right triangles as fresinha said and one on them is
3-4-5

others are
5-12-13
6-8-10
8-15-17
7-24-25
etc

basically all that satisfy pythagorean theorem

here we need to recognize (visually) that hypothenuse 16+9=25 stands approximatelly in 3-4-5 ratio
and therefore the explanation follows
hypo = 25
therefore height is (15*15)-(9*9)=sqrt144=12

plug in the triangle formula and calculate 300/2=150

GMAT TIGER · Answer

How do you use those shortcuts such as "3-4-5"? Can you be more elabroative?

I could not do so.

scthakur · Answer

I will solve this using the similar triangles. PQS and QSR are similar triangles such that
PS/SQ = SQ/SR
or SQ = sqrt(PS*SR) = 4*3 = 12

Hence, area = 1/2*12*25 = 150.

manudhimanisb09 · Answer

scthakur..
how did u figure out that PQS and QSR are similar triangles ??

GMAT TIGER · Answer

Intresting

but on what basis you say that PS/SQ = SQ/SR is true? :roll:

mbajingle · Answer

Similar triangles. Its a theorem which says if the angles of two triangle are same then the corresponding sides of the triangle will be in proportion.

GMAT TIGER · Answer

No dispute on these basics. But how do you show that the corresponding angles are same?

scthakur · Answer

Ok, here we go.

Between triangles PQR and PQS
angle PQR = angle PSQ = 90 degree.
angle QPS is common.
Hence, the third angle QRP equals angle PQS and this also makes triangles PQS and QSR similar.

Hope, this clarifies.

PS : Triangle

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards