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If the hypotenuse of an isosceles right triangle is , what i
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20 Sep 2018, 16:46
20 Sep 2018, 16:46
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Expert Reply
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Question Stats:
77% (00:47) correct
22% (00:57) wrong based on 63 sessions
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If the hypotenuse of an isosceles right triangle is \(8\sqrt{2}\), what is the area of the triangle?
(A) 18
(B) 24
(C) 32
(D) 48
(E) 64
(A) 18
(B) 24
(C) 32
(D) 48
(E) 64
Re: If the hypotenuse of an isosceles right triangle is , what i
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20 Sep 2018, 21:49
20 Sep 2018, 21:49
answer should be c not b if b is answer, explain why??
Re: If the hypotenuse of an isosceles right triangle is , what i
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24 Sep 2018, 08:32
24 Sep 2018, 08:32
1
Expert Reply
Explanation
All isosceles right triangles (or 45–45–90 triangles) have sides in the ratio of \(1 : 1 : \sqrt{2}\).
Thus, an isosceles right triangle with hypotenuse \(8\sqrt{2}\) has sides of \(8\), \(8\), and \(8\sqrt{2}\).
Use the two legs of 8 as base and height of the triangle in the formula for area:
\(A=\frac{b \times h}{2}=\frac{8 \times 8}{2}=32\)
All isosceles right triangles (or 45–45–90 triangles) have sides in the ratio of \(1 : 1 : \sqrt{2}\).
Thus, an isosceles right triangle with hypotenuse \(8\sqrt{2}\) has sides of \(8\), \(8\), and \(8\sqrt{2}\).
Use the two legs of 8 as base and height of the triangle in the formula for area:
\(A=\frac{b \times h}{2}=\frac{8 \times 8}{2}=32\)
