In the first question we can solve using the Pythagorean theorem. It states that the hypotenuse in a right triangle or the longest side of the triangle, squared is equal to the other 2 sides, squared. Its expressed as so: C^2 = A^2 + b^2 where c is the hypotenuse and a and b are the other sides oft eh triangle.

Therefore,

15^2 = 12^2+x^2

225=144+x^2

81=x^2

x=9

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11. x=12

In this figure, there are 2 right triangles on the sides of the square. If we can find the lengths of the base of both triangles then we can find x using the Pythagorean theorem. the total base is 21 and the square is 11. 11+a+b=21. We can assume that both triangles are congruent and therefore we can solve this equation:

11+a+b=21

a+b=10

5+5=10

b=5

a=5

The bases of the two triangles are 5 and the hypotenuse is 13. Now we can solve using the Pythagorean theorem:

c^2 = a^2+b^2

13^2=5^2+x^2

169=25+x^2

144=x^2

144= 12 x 12

x=12

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12.

The diagnol of a triangle is the hypotenuse and since the length is the square root of 3, we have all the information we need.

c^2 = a^2+b^2

2^2 = (square root of 3)^2+b^2

4=3+b^2

1=b^2

b=1

Step-by-step explanation:

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2 years ago