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4 years ago

The value of x must be greater than

Mathematics

1 answer:

frozen [14]4 years ago

4 0

Using the Pythagorean theorem:

12^2 + x^2 = 15^2

144 + x^2 = 225

x^2 = 225 - 144

x^2 = 81

x = sqrt(81)

x = 9

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

13.

$1.\overline{52}\\$ = 1.525252...

Let x = 1.525252...

10x = 15.2525252....

100x = 152.525252...

100x - x = 151.00

99x = 151

$x = \frac{151}{99}\\\\or\\\\x = 1 \frac{52}{99}$

14.

4x + 10 = 8x - 26 [ corresponding angles are congruent ]

4x - 8x = - 26 - 10

- 4x = - 36

$x = \frac{-36}{-4} \\\\x = 9$

15.

Given breadth of a rectangle is ( 2/3) its length.

Let the length be x

Therefore, breadth = ( 2 /3) of x

$= \frac{2}{3} \times x\\\\=\frac{2}{3}x$

Given perimeter = 40m

Perimeter of a rectangle = 2( length + breadth)

$40 = 2 (x + \frac{2}{3}x )\\\\\frac{40}{2} = \frac{2}{2}(x + \frac{2}{3}x)\\\\20 = x + \frac{2}{3}x\\\\20 = \frac{3x + 2x}{3}\\\\20 \times 3 = 5x \\\\x = \frac{60}{5}\\\\x = 12\\\\Therefore, Length = x = 12 \ m \ and \ breadth = \frac{2}{3}x = \frac{2}{3} \times 12 = 8 \ m$

16.

Sum of the angles of a triangle = 180°

Given ratio = 2 : 3 : 4

Sum of the ratio = 9

Therefore,

$first \ angle = \frac{2}{9} \times 180 = 2 \times 20 = 40 ^\circ\\\\Second \ angle = \frac{3}{9} \times 180 = 3 \times 20 = 60^\circ\\\\Third angle = \frac{4}{9} \times 180 = 4 \times 20 = 80^\circ$