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MBAlad
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What is the area of triangle A 10 Dec 2006, 09:07
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What is the area of triangle A?



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trivikram
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What is the area of triangle A Updated on: 10 Dec 2006, 09:54
Originally posted by trivikram on 10 Dec 2006, 09:42.
Last edited by trivikram on 10 Dec 2006, 09:54, edited 2 times in total.
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Is it 96...

OK the diagonal is 25

Let the length of the diagonal till the perpendicular line be 25-x and from that to the next vertex be x (so sum is 25)

So the length of perpendicular is sqrt(15^2 -x^2)

(25-x)^2 + (15^2 -x^2) = 400

Solve for x and get the x = 9

So area = 1/2*16*12 = 96
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MBAlad
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What is the area of triangle A 10 Dec 2006, 09:44
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I'll let a few other people post before revealing OA

Can you all please show working.
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mst
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What is the area of triangle A 10 Dec 2006, 09:56
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I redrew the figure with vertices marked. And if I am understanding it correctly, Triangle A is KLP in my figure.

Area (KNM) = Area (KLM) = 1/2 x15x20 = 150
Area (KLM) = 1/2 KM x LP = 150

KM^2 = 15^2+20^2 = 625
KM = 25

Therefore LP = 2 x 150/25 = 12

KP = sq root (KL^2 - LP^2) = (400 - 144)^1/2 = 16

Area of triangle A = 1/2 x KP x LP = 1/2 * 16* 12 = 96
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Sumithra
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What is the area of triangle A 10 Dec 2006, 10:05
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Area of the rectangle=20*15=300

Area of the bigger triangle=20*15/2=150
Area of the smaller traingle=12*9/2=54 (since hypo=5*3 of 3:4:5)

Area of A=300-(150+54)=96
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What is the area of triangle A 10 Dec 2006, 12:18
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Good work chaps - OA is 96

Way I did it - I'll refer to your diagram mst (it's better than mine :oops: )

Triangle KLP and KNM are similar since angle KMN = angle LKP

Looking at right triangle KNM you can see it's sides are in the ration 3:4:5 (multiplied by 5) ie 15:20:25(KM)

Therefore sides of triangle KLP must also be in this ratio (multiplied by 4) ie 12:16:20

So 12*16/2 = 96



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