Question

FIND AC2 IN THE FIGURED ALONGSIDE​

Answer 1

Answer:

• In ∆ABC & ∆ABD

AB = AB — common side

∠ B = ∠ B — common Angle (90°)

BC = CD — Given Equal

∆ABC ~ ∆ABD — SAS Similarity

• According to the Question Now :

⇒ AB/AC = AC/AD

⇒ 5 m/AC = AC/9 m

⇒ 5 m × 9 m = AC × AC

⇒ AC² = 45 m²

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is 45 m²

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$\huge\sf\blue{Given}$

✭ ∆ABC & ∆ABD are right angled triangles, right angled at B

✭ AB = 5 cm

✭ BC = CD

✭ AD = 9 cm

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$\huge\sf\gray{To \:Find}$

◈ The value of AC²?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Concept}}$

So we shall here prove that two triangles are similar using the SAS similarly and then later on as we know Corresponding sides of similar triangles are proportional we may use that to get our final answer

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☯ $\underline{\textsf{As Per the Question}}$

In ∆ABC & ∆ABD

➝ $\sf AB = AB$ «« Common »»

➝ $\sf \angle B = \angle$ B «« 90° »»

➝ $\sf BC = CD$ «« Given »»

$\sf \therefore \triangle ABC \sim \triangle ABD$ «« SAS »»

So then,

➳ $\sf \dfrac{AB}{AC} = \dfrac{AC}{AD}$

➳ $\sf \dfrac{5}{AC} = \dfrac{AC}{9}$

➳ $\sf 5\times 9 = AC \times C$

➳ $\sf \orange{AC^2 = 45 \ m^2}$

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✪ $\sf \underline{\sf Know \ More}$

Basic Proportionality Theorem (BPT)

◕ When a line is drawn parallel to one side of a triangle meeting the other two sides in distinct points,then the other two sides will be divided in the same Ratio

Areas of Similar Triangles

◕ The ratio of the areas of similar triangles are equal to the square of the ratio of their corresponding sides

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