Question

with explaination please

Answer 1

$\huge\mathcal\colorbox{lavender}{{\color{b}{✿Yøur-Añswer♡}}}$

$\large\bf{\underline{\red{illusion}}}$

10) ∠ADB = 90° and AC = AB = 26 cm

AD = 24 cm

To find :

Length of BC In right angled ∆ADC

AB = 26 cm, AD = 24 cm

According to Pythagoras Theorem,

$AC^2=AD^2+DC^2$

$26^2=24^2+DC^2$

$676=576+DC^2$

$DC^2=100$

$DC=\sqrt{100}=10\ cm$

∴ Length of BC = BD + DC

━━━━━━━━❪❐━━━━━━━

☆✿╬ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ᴜ╬✿☆

$\huge\bold\star{mark \: as \: brainliest}\star$

Answer 2

Throughout these questions, we must remember the Pythagoras Theorem.

It states that the square on the hypotenuse of a right-angled triangle is equal to sum of the squares on the other two sides of the triangle.

$\boxed{\sf{s^{2}+s^{2}=h^{2}}}$

Also, the hypotenuse is the longest side in a right-angled triangle, opposite to the right angle.

Let's begin!

Question 8

Given:

• AB = 9 cm
• BC = 40 cm
• AC = 41 cm >> hypotenuse

To show:

It is a right-angled triangle

Solution:

By the Pythagoras Theorem, sum of the squares on the sides AB and BC will be equal to the square on hypotenuse AC. Which means,

AB² + BC² should be = AC²

The LHS

⇒ 9² + 40²

⇒ 81 + 1600

⇒ 1681

The RHS

⇒ 41²

⇒ 1681

LHS = RHS

So, AB² + BC² = AC².

Hence, proved that triangle ABC is a right-angled triangle.

Question 9

Given:

• ∠ACB = 90° = ∠ACD >> right-angled triangle
• AB = 10 cm
• BC = 6 cm
• AD = 17 cm

To find:

Lengths of

• AC
• CD

Solution:

Finding AC

We have the measures of one side and the hypotenuse of the triangle. We can easily find AC, the other side of triangle ABC, by the Pythagoras Theorem. So,

⇒ AC² + BC² = AB²

⇒ AC² + 6² = 10²

⇒ AC² + 36 = 100

⇒ AC² = 100 - 36

⇒ AC² = 64

⇒ AC = 8

Therefore, AC measures 8 cm.

Finding CD

Now that we have found the measure of AC, we have the measures of one side (CD) and the hypotenuse (AD) of the triangle. By applying the Pythagoras Theorem,

⇒ AC² + CD² = AD²

⇒ 8² + CD² = 17²

⇒ 64 + CD² = 289

⇒ CD² = 289 - 64

⇒ CD² = 225

⇒ CD = 15

Therefore, CD measures 15 cm.

Question 10

Given:

• ADB = 90° >> right-angled triangle
• AC = AB = 26 cm
• BD = DC
• AD = 24 cm

To find:

• Length of BC

Solution:

In right-angled triangle ADB,

• AB = 26 cm (given)
• AD = 24 cm (given)

We have the measures of one side and the hypotenuse of the triangle. Applying the Pythagoras Theorem,

⇒ AD² + BD² = AB²

⇒ 24² + BD² = 26²

⇒ 576 + BD² = 676

⇒ BD² = 676 - 576

⇒ BD² = 100

⇒ BD = 10

So, BD measures 10 cm.

We are given that BD = DC, so DC = 10 cm as well.

Now, length of BC = BD + DC

                                  10 + 10

                                  20 cm

Therefore, the length of BC is 20 cm.