Question

Q.1. What is the length of the side x?
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Answer 1

Answer:

x = 2√11cm

Step-by-step explanation:

Since, the triangle with sides 6cm and 8cm is right-angled.

Therefore, by pythagoras theorem, the length of the third side would be 10cm.

Similarly, the triangle formed with 10cm and 12cm as its sides is also right-angled, so, again by using pythagoras theorem,

The side x =  144-100 = √44 = 2√11cm

Hope this helps.....

Answer 2

Length of side x is 2√11 cm.

Given:

• A figure.

To find:

• Value of x.

Solution:

Concept to be used:

In a right triangle the relationship between the sides are

$\bf Hypotenuse ^{2} =Base^{2} +Perpendicular^{2}$

Step 1:

Calculate the length of side AC.

In the attached figure;

∆ABC is right angle triangle, right angle at B.

So,

Let, Base (BC)= 8cm

Perpendicular (AB)=6 cm

Apply Pythagoras theorem in ∆ABC.

$AC = \sqrt{ {8}^{2} + {6}^{2} }$

$AC = \sqrt{64 + 36 }$

$AC = \sqrt{100 }$

$\bf AC =10 \: cm$

Thus,

Length of AC is 10 cm.

Step 2:

Calculate the length of x.

Again, ∆ACD is right angle triangle, right angle at C.

So,

Let, Base (CD)= x cm

Perpendicular (AC)=10 cm

Hypotenuse (AD)=12 cm

Apply Pythagoras theorem in ∆ACD.

$( {12)}^{2} = ( {10)}^{2} + {x}^{2}$

${x}^{2} = 144 - 100$

${x}^{2} = 44$

$x = \sqrt{4 \times 11} \: cm$

$\bf x = 2 \sqrt{11} \: cm$

Thus,

Length of side x is 2√11 cm.

Learn more:

1) If length of a diagonal of rhombus is 30 cm ahd its 240sq cm find it perimeter

https://brainly.in/question/9094902

2) A(1,7), B(2,4), C(k,5) are the vertices of a right angled ΔABC,Find k, if ∠C is a right angle

https://brainly.in/question/5078319

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