The sides of a right triangle are equal to A=3 cm, B=4 cm. The hypotenuse of a second triangle similar to the first one is 15 cm. Find sides of the second triangle.
Firstly based on the Pythagoras Theorem which claims that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we will find the hypotenuse of the first triangle. To make the calculations easier we will mark hypotenuse with C. C2=A2+B2, C2=32+ 42, C2=9+16, C2=25, C=5 cm. The hypotenuse of the first triangle is 5 cm. Furthermore, we know that the hypotenuse of the second triangle is 15 cm and both triangles are similar. The similarity of triangles means that they have equal angles but they change in size of sides. In similar triangles, corresponding sides are always in the same ratio. Thus, we are going to find the ratio of our triangles. RATIO= C2(second hypotenuse)/C1(first hypotenuse), RATIO=15/5, RATIO= 3 times the sides of the second triangle are three times bigger than the first triangle. Let's find the sides of the second triangle: A2=33, A2=9 cm, B2=43, B2=12 cm. As we can see the sides of the second triangle are 9 and 12 cm.
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