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Class 10 > Learn Mathematics > If the areas of two similar triangles are in ratio...
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If the areas of two similar triangles are in ratio 25 : 64, write the ratio of their corresponding sides.

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7to 10 science and maths11and 12 physics and maths

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Concept:::The ratio between corresponding sides of two similar triangles is same as the ratio of square root of their areas. Solution:::Ratio of the sides =root25:root64 =5:8.
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Tutor

The ratio of the two corresponding side of two similar triangle is equal to the square root of the ratio of the area of the two triangle..so ratio is 5:8
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Let the base and height of triangles are b,h and B,H respectively. The ratio of the area=25:64 => (b*h)/(B*H) = 25/64 => (b/B)*(h/H) = 25/64 ............(1) Since the triangles are similar, the ratio between corresponding side are equal. => b/B = h/H .........................(2) applying...
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Let the base and height of triangles are b,h and B,H respectively. The ratio of the area=25:64 => (b*h)/(B*H) = 25/64 => (b/B)*(h/H) = 25/64 ............(1) Since the triangles are similar, the ratio between corresponding side are equal. => b/B = h/H .........................(2) applying (2) in (1), (b/B)^2 = 25/64 => b/B = +(5/8) or -(5/8) Since this is the ratio of the sides of two triangles, we take the positive roots. => b:B = 5:8 , which is the required ratio of corresponding sides of the above pair of similar triangles. read less
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Area of triangle=1/2×base×height. 25:64. Sides ratio. 25×2:64×2. 59/128=25/64=12.5/32=6.25/18=1/3. Ratio of sided 1: 3
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area of triangle1/area of triangle2=(side1)^2/(side)^2
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If the ratio of the sides is a/b, then the ratio of the areas is (a^2)/(b^2) In our case, a^2 = 25, so a = 5. Also, b^2 = 36 which means b = 6 So the ratio of a pair of corresponding sides is 5/6
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