Question

Help needed very much

Answer 1

10. x = 13

11. x = √65

12. x = 12

13. x = 17

14. x = 8

Explanation:

10. This triangle is isosceles, so the base is divided in 2 equal parts (one part is 0,5 × 24 = 12)

Use the Pythagorean theorem:

`{x}^(2) = {5}^(2) + {12}^(2) = 25 + 144 = 169`

`x > 0`

`x = √(169) = 13`

11. Opposite sides of a rectangle are equal

Use the Pythagorean theorem:

`{x}^(2) = {7}^(2) + {4}^(2) = 49 + 16 = 65`

`x > 0`

`x = √(65)`

12. This figure is formed from a rectangle and a right triangle

19 - 10 = 9 (bottom side of a triangle)

Let's find x by using the Pythagorean theorem:

`{x}^(2) = {15}^(2) - {9}^(2) = 225 - 81 = 144`

`x > 0`

`x = √(144) = 12`

13. This triangle contains two right triangles

The construction of the smaller triangle can be found by using the Pythagorean theorem:

`{10}^(2) - {6}^(2) = 100 - 36 = 64`

`√(64) = 8`

Now, let's find x by using the Pythagorean theorem:

`{x}^(2) = {8}^(2) + {15}^(2) = 64 + 225 = 289`

`x > 0`

`x = √(289) = 17`

14. The diagonal of a rectangle divides it into two right triangles

Since the diagonal is not perpendicular, it is the hypotenuse of the triangles

Use the Pythagorean theorem to find the other length:

`{x}^(2) = {10}^(2) - {6}^(2) = 100 - 36 = 64`

`x > 0`

`x = √(64) = 8`