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On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a

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On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a  [#permalink]

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New post 26 Jan 2016, 05:22
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On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the area of MNP in square units?

A. 312
B. 240
C. 120
D. 60
E. 30

Attachment:
2016-01-24_1653.png
2016-01-24_1653.png [ 2.46 KiB | Viewed 1196 times ]

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Re: On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a  [#permalink]

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New post 26 Jan 2016, 05:32
In right angled \(\triangle\) NMP
NM^2 = NP^2 - MP^2
= 26^2 - 24^2
=676 - 576
= 100
NM= 10

area of \(\triangle\) MNP = 1/2 *NM *MP
= 1/2 *10 * 24
= 120

Answer C
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Re: On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a  [#permalink]

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New post 26 Jan 2016, 23:02
Bunuel wrote:
Image
On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the area of MNP in square units?

A. 312
B. 240
C. 120
D. 60
E. 30

Attachment:
2016-01-24_1653.png


First simply calculate MN using Pythagoras Theorem i.e. h^2=p^2+b^2
MN=\sqrt{26^2-24^2}
=10
Now
Area of MNP=1/2*MN*MP=1/2*24*10=120 units
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Re: On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a  [#permalink]

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New post 27 Jan 2016, 01:15
Skywalker18 wrote:
In right angled \(\triangle\) NMP
NM^2 = NP^2 - MP^2
= 26^2 - 24^2
=676 - 576
= 100
NM= 10

area of \(\triangle\) MNP = 1/2 *NM *MP
= 1/2 *10 * 24
= 120

Answer C

yes Answer is 120 [C]
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Re: On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a  [#permalink]

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New post 27 Jan 2016, 02:46
1
Bunuel wrote:
Image
On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the area of MNP in square units?

A. 312
B. 240
C. 120
D. 60
E. 30

Attachment:
2016-01-24_1653.png


It is good to remember the first few pythagorean triplets and their multiples.
Note that 24 and 26 are second positive multiplies of 12 and 13. So this must be the 5, 12, 13 triplet. The third side must be 5*2 = 10

Area of MNP = (1/2)*10*24 = 120 square units.

Answer (C)
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Re: On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a  [#permalink]

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New post 08 Sep 2018, 14:24
Skywalker18 wrote:
In right angled \(\triangle\) NMP
NM^2 = NP^2 - MP^2
= 26^2 - 24^2
=676 - 576
= 100
NM= 10


I like to think of this step as
= 26^2 - 24^2
= (26 - 24)(26 + 24)
=2*50
=100

I find it saves time
Re: On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a &nbs [#permalink] 08 Sep 2018, 14:24
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