3 years ago

Lengths of Rectangles

Mathematics

1 answer:

Furkat [3]3 years ago

6 0

Answer:

AB = 5

BC = 12

AC = 13

Step-by-step explanation:

A rectangle is a quadrilateral and therefore, opposite sides are parallel and congruent to each other. Thus:

AB = CD = 12

AB = 12

BC = AD = 5

BC = 5

AC is a diagonal of the rectangle, use Pythagorean theorem to find it's length as follows:

AC² = AD² + CD²

Plug in the values

AC² = 5² + 12²

AC² = 169

AC = √169

AC = 13

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Alik [6]

x = 1

Answer:

$m\angle XVW = 100\degree$

Step-by-step explanation:

In the first figure, FP is the bisector of $\angle DFE$

$\therefore m\angle 1 = m\angle 2\\\therefore 44x + 1 = 46x - 1\\\therefore 1 + 1 = 46x - 44x\\\therefore 2 = 2x\\\therefore \frac{2}{2} = x \\\huge \red {\boxed {\therefore x = 1}}$

In the second figure, VP is the bisector of $\angle XVW$

$\therefore m\angle 1 = m\angle 2\\\therefore 12x + 2 = 11x +6\\\therefore 12x - 11x = 6 - 2\\\therefore x = 4\\\because m\angle XVW = m\angle1 + m\angle 2\\\therefore m\angle XVW = 12x + 2 + 11x +6\\\therefore m\angle XVW = 23x + 8\\\therefore m\angle XVW = 23\times 4+ 8\\\therefore m\angle XVW = 92+ 8\\\huge \purple {\boxed {\therefore m\angle XVW = 100\degree}} \\$