Question

5. ΔABC is right angled at B. AB = 3 cm and BC = 4 cm. Then, length of AC will be a) 25 cm

b) 5 cm c) 7 cm d) 6 cm

6. Find the area of a square whose side is 6 cm.​

Answer 1

Step-by-step explanation:

Since, <1 + <2 = 90 deg ( given)

& <3 + <2 = 90 deg ( by angle sum property of a triangle)

=> <1 = <3

So, tri BDA ~ tri CDB ( by AA similarity criterion)

=> BD/CD = DA/DB = BA/CB ( csst )

Or, BD/x = (5-x)/BD = 3/4

=> 3x = 4BD

=> BD = 3x/4 ……………….. (1)

Since (5-x)/BD = 3/4 (csst)

So, (5-x)/(3x/4) = 3/4

=> 80 - 16x = 9x

=> 25x = 80

=> x = 80/25 = 16/5 = 3.2 cm

Since BD = 3x/4 = (3 * 3.2)/4 = 3* 0.8 = 2.4

BD = 2.4 cm

If the angle B = 90°, AC is the hypotenuse and is equal to 5 cm by Pythagoras theorem.

Area of ∆ ABC = (1/2)(AB)(BC)

= (1/2)(3)(4) = 6 cm^2 …….(1)

If the hypotenuse is taken as the base and BD as the height then the area of the ∆ABC

= (1/2)(AC)(BD)

=> (1/2)(5)(BD) = 6 from (1)

=> BD = 12/5 = 2.4 cm.

Answer 2

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❥First Question

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Given

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• ∠B = 90°

• AB = 3cm

• BC = 4cm

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To Calculate

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• Measure of AC

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Solution

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ABC is a right angle triangle.

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So, by Pythagorous Theorem

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

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$\bf \implies{Hypotenuse}^{2} = {3}^{2} + {4}^{2}$

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$\bf \implies{Hypotenuse}^{2} =9 + 16$

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$\bf \implies{Hypotenuse}^{2} =25$

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$\bf \implies{Hypotenuse} = \sqrt{25}$

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$\bf \implies{Hypotenuse} =5cm$

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Therefore, Measure of AC is 5cm.

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❥Second Question

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Given

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• Side of Square = 6cm

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To Find

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• Area of Square

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Solution

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$\bf Area = {Side}^{2}$

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$\bf = 6cm \times 6cm$

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$\bf = {36cm}^{2}$

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Hence, Area of square is 36 sq. cm.