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

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Math Expert
Joined: 02 Sep 2009
Posts: 50671
On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a  [#permalink]

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26 Jan 2016, 04:22
00:00

Difficulty:

15% (low)

Question Stats:

86% (01:24) correct 14% (01:18) wrong based on 66 sessions

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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 [ 2.46 KiB | Viewed 1360 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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26 Jan 2016, 04:32
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

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Joined: 27 Dec 2015
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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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26 Jan 2016, 22:02
Bunuel wrote:

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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27 Jan 2016, 00:15
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

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Joined: 16 Oct 2010
Posts: 8562
Location: Pune, India
Re: On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a  [#permalink]

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27 Jan 2016, 01:46
1
Bunuel wrote:

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.

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Intern
Joined: 26 Jul 2018
Posts: 1
Re: On MNP, MN is perpendicular to MP, MP = 24, and NP = 26. What is the a  [#permalink]

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08 Sep 2018, 13:24
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, 13:24
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