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The diagram below shows a triangle and some of its dimensions.

20 cm-
tcm
15 cm
What is the value of t?
30 cm
40 cm
35 cm
25 cm

The diagram below shows a triangle and some of its dimensions. 20 cm- tcm 15 cm What-example-1

1 Answer

7 votes

Answer:

25 cm

Explanation:

You want to know the length of the hypotenuse in a right triangle with legs 15 cm and 20 cm.

Pythagorean triple

The given leg lengths have the ratio ...

15 : 20 = 3 : 4 . . . . . . . scale factor of 5

This means they are part of a 3 : 4 : 5 right triangle.

The length "t cm" is 5·5 cm = 25 cm.

The value of t is 25.

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Additional comment

In case you've never heard of a {3, 4, 5} right triangle, you can figure the missing hypotenuse from the Pythagorean theorem:

c² = a² +b²

t² = 15² +20² = 225 +400 = 625

t = √625 = 25

The {3, 4, 5} Pythagorean triple is used repeatedly in algebra, geometry, and trig problems, along with some others: {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. These can appear as multiples of the basic triple, as here, where the multiple is 5 × {3, 4, 5} = {15, 20, 25}.

User Cephron
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