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# Isosceles right triangle ABC has an area of 72. What is its perimeter?

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Math Expert
Joined: 02 Sep 2009
Posts: 47166
Isosceles right triangle ABC has an area of 72. What is its perimeter?  [#permalink]

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10 Apr 2018, 00:04
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Difficulty:

35% (medium)

Question Stats:

84% (00:51) correct 16% (01:36) wrong based on 51 sessions

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Isosceles right triangle ABC has an area of 72. What is its perimeter?

A. 12+6√2
B. 16+8√2
C. 18+9√2
D. 20+10√2
E. 24+12√2

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Re: Isosceles right triangle ABC has an area of 72. What is its perimeter?  [#permalink]

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10 Apr 2018, 00:22
1
Bunuel wrote:
Isosceles right triangle ABC has an area of 72. What is its perimeter?

A. 12+6√2
B. 16+8√2
C. 18+9√2
D. 20+10√2
E. 24+12√2

Ans : E
Area of triangle = $$1/2 *b* h$$
as it is isosceles right triangle, b=h ,
So $$72=1/2 *h* h$$
$$144 =h^2$$
$$h= 12$$

$$hypotenuse = 12√2$$
Perimeter would be $$2*12+12√2$$ i.e $$24+12√2$$
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Re: Isosceles right triangle ABC has an area of 72. What is its perimeter?  [#permalink]

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10 Apr 2018, 00:24
Bunuel wrote:
Isosceles right triangle ABC has an area of 72. What is its perimeter?

A. 12+6√2
B. 16+8√2
C. 18+9√2
D. 20+10√2
E. 24+12√2

As all we're given is the area, we'll work with area-related equations.
This is a Precise approach.

Since ABC is a right triangle then its area is the product of its legs times two.
Since it is isosceles, its legs are equal to each other.
So, if x is the lenght of a leg than x^2/2 = 72 --> x^2 = 144 --> x = 12.
Then the hypotenuse is 12√2 (as this is a 90-45-45 triangle) so the perimeter is 24+12√2

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Re: Isosceles right triangle ABC has an area of 72. What is its perimeter? &nbs [#permalink] 10 Apr 2018, 00:24
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