the perimeters of 2 similar triangles are 40cm and 50cm respectively, find the ratio of the area of the first triangle to the area of the 2nd triangle.
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Perimeter of 1st triangle = 40 cm
Perimeter of 2nd triangle = 50 cm
Ratio of squares of perimeters of two triangles is equal to the ratio of areas of both triangles.
\frac{ {(perimeter \: of \: 1st \: triangle)}^{2} }{ {(perimeter \: of \: 2nd \: triangle)}^{2} } = \frac{area \: of \: 1st \: triangle}{area \: of \: 2nd \: triangle}(perimeterof2ndtriangle)2(perimeterof1sttriangle)2=areaof2ndtriangleareaof1sttriangle
\frac{ {40}^{2} }{ {50}^{2} } = \frac{1600}{2500} = \frac{16}{25}502402=25001600=2516
Ratio of areas = 16:25
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Perimeter of 2nd triangle = 50 cm
Ratio of squares of perimeters of two triangles is equal to the ratio of areas of both triangles.
\frac{ {(perimeter \: of \: 1st \: triangle)}^{2} }{ {(perimeter \: of \: 2nd \: triangle)}^{2} } = \frac{area \: of \: 1st \: triangle}{area \: of \: 2nd \: triangle}(perimeterof2ndtriangle)2(perimeterof1sttriangle)2=areaof2ndtriangleareaof1sttriangle
\frac{ {40}^{2} }{ {50}^{2} } = \frac{1600}{2500} = \frac{16}{25}502402=25001600=2516
Ratio of areas = 16:25
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