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What is the difference between the hypotenuse and the base of an isosceles right triangle that has an area of 392 m2 (use 2=1.4)?
11.9 m
10.9 m
11.2 m
12.4 m
11.2 m
Since Area = 392, a² = 784, so a = 28. Then hypotenuse h = 28 × 1.4 = 39.2. Difference = 39.2 - 28 = 11.2.
Area of an isosceles right triangle = 392 m², √2 = 1.4
Area=21×a2, h=a2
Since Area = 392, a² = 784, so a = 28. Then hypotenuse h = 28 × 1.4 = 39.2. Difference = 39.2 - 28 = 11.2.
Students often confuse the base with the hypotenuse or fail to identify that in an isosceles right triangle, the two legs are the 'base' and 'height' of equal length.
Identify triangle properties
For an isosceles right triangle, the two perpendicular sides (legs) are equal. Let the length of each leg be a. The area is given by Area=21×a2.
392=21a2
Calculate leg length a
Solve for a2: a2=392×2=784. Taking the square root, a=784=28.
a=28
Calculate hypotenuse h
The hypotenuse h of an isosceles right triangle is a2. Given 2=1.4, we compute h=28×1.4.
h=39.2
Find the difference
The difference between the hypotenuse and the base (leg) is h−a=39.2−28=11.2.
39.2−28=11.2
C is correct because the hypotenuse is 39.2 m and the base is 28 m, resulting in a difference of 11.2 m.
This concept is foundational in Trigonometry for understanding the ratio of sides in a 45°−45°−90° triangle.
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