Question

Can somebody help me please

Answer 1

Answer:

x = 7

Step-by-step explanation:

The 2 right triangles are similar by the AA postulate, then the ratios of corresponding sides are in proportion, that is

$\frac{x}{4}$ = $\frac{3.5}{2}$ ( cross- multiply )

2x = 14 ( divide both sides by 2 )

x = 7

Answer 2

Will recommend to see attached picture as name of angles are based on it.

We can only find value of x if both triangles i.e triangle DOC and triangle AOB are similar.

$\sf \underline{In \: \triangle \: DOC \: and \: \triangle\:AOB: }$

$\sf1. \angle DOC = \angle AOB$

Reason :-

VOC (Vertically opposite angle)

How to recognize either it is VOC (Vertically opposite angle) or not?

So it's basically very easy to recognize, when ever u see lines intersect each other just like a multiply sign ( × ) either horizontal or parallel they are considered as VOC ans are always equal.

$\sf2. \angle CDO = \angle BAO$

Reason:-

Both are of 90°.

So how we recognized that these both angles were in 90°?

When ever you see that angle is marked in square ( □ ) like shape instead of curve shape then it means the angle is 90°.

$\sf\triangle \: DOC\simeq \triangle\:AOB:$

By :- AA (angle angle)

Now Finally Let's find value of x.

$\dashrightarrow \sf\dfrac{DC}{AB} = \dfrac{OC}{OB} = \dfrac{OD}{OA}$

Reason :- Corresponding sides of similar triangle are in proportion.

So:-

$\dashrightarrow \sf\dfrac{DC}{AB} = \dfrac{OC}{OB}$

$\dashrightarrow \sf\dfrac{2}{3.5} = \dfrac{4}{x}$

$\dashrightarrow \sf\dfrac{3.5}{2} = \dfrac{x}{4}$

$\dashrightarrow \sf\dfrac{35}{2 \times 10} = \dfrac{x}{4}$

$\dashrightarrow \sf\dfrac{ \cancel{35}}{2 \times \cancel{10}} = \dfrac{x}{4}$

$\dashrightarrow \sf\dfrac{7}{2 \times 2} = \dfrac{x}{4}$

$\dashrightarrow \sf\dfrac{4 \times 7}{2 \times 2} = x$

$\dashrightarrow \sf\dfrac{ \cancel4 \times 7}{\cancel2 \times 2} = x$

$\dashrightarrow \sf\dfrac{ 2 \times 7}{1 \times 2} = x$

$\dashrightarrow \sf\dfrac{\cancel 2 \times 7}{1 \times \cancel2} = x$

$\dashrightarrow \sf\dfrac{1 \times 7}{1 \times 1} = x$

$\dashrightarrow \sf\dfrac{7}{1 } = x$

$\dashrightarrow \sf7= x$

$\dashrightarrow \bf x = 7$

.°. length of x is equal to 7(unit)