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Lesson Example Discussion Quiz: Class Homework

Step-3

Title: Quadrilaterals (Rhombus, Square)

Grade: 6-a Lesson: S2-L5

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	ABCD is a rhombus whose diagonals intersect at O. If AB = 13 cm, diagonal BD = 24 cm, find the length of diagonal AC.
2	Step	We know in rhombus, diagonals bisect each other at the right angle In ΔAOB	BO = \$(BD)/2\$ = \$24/2\$ = 12 cm
3	Formula	Using Pythagoras’s theorem in ΔAOB	\$AB^2 = AO^2 + BO^2\$
4	Step	Substitute the value in the formula	⇒ \$13^2 = AO^2 + 12^2\$ ⇒ \$169 = AO^2 + 144\$
5	Step	Now simplify the equation	⇒ \$AO^2 = 169 - 144\$ ⇒ \$AO^2 = 25\$
6	Step	Apply square root on both sides	⇒ \$\sqrt(AO^2) = \sqrt(25)\$ ⇒ AO = 5 cm
7	Step	The length of diagonal AC is 5 x 2 = 10 cm.
8	SumUp	Can you summarize what you’ve understood in the above steps?
9	Choice.A	This is correct because it match the calculated length for diagonal AC, which is 10 cm by using Pythagoras’s theorem	10 cm
10	Choice.B	This is not correct because it does not match the calculated length for diagonal AC, which is 10 cm by using Pythagoras’s theorem	12 cm
11	Choice.C	This is not correct because it does not match the calculated length for diagonal AC, which is 10 cm by using Pythagoras’s theorem	14 cm
12	Choice.D	This is not correct because it does not match the calculated length for diagonal AC, which is 10 cm by using Pythagoras’s theorem	16 cm
13	Answer	Option	A
14	SumUp	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

ABCD is a rhombus whose diagonals intersect at O. If AB = 13 cm, diagonal BD = 24 cm, find the length of diagonal AC.

Step

We know in rhombus, diagonals bisect each other at the right angle In ΔAOB

BO = \$(BD)/2\$ = \$24/2\$ = 12 cm

Formula

Using Pythagoras’s theorem in ΔAOB

\$AB^2 = AO^2 + BO^2\$

Step

Substitute the value in the formula

⇒ \$13^2 = AO^2 + 12^2\$

⇒ \$169 = AO^2 + 144\$

Step

Now simplify the equation

⇒ \$AO^2 = 169 - 144\$

⇒ \$AO^2 = 25\$

Step

Apply square root on both sides

⇒ \$\sqrt(AO^2) = \sqrt(25)\$

⇒ AO = 5 cm

Step

The length of diagonal AC is 5 x 2 = 10 cm.

SumUp

Can you summarize what you’ve understood in the above steps?

Choice.A

This is correct because it match the calculated length for diagonal AC, which is 10 cm by using Pythagoras’s theorem

10 cm

Choice.B

This is not correct because it does not match the calculated length for diagonal AC, which is 10 cm by using Pythagoras’s theorem

12 cm

Choice.C

This is not correct because it does not match the calculated length for diagonal AC, which is 10 cm by using Pythagoras’s theorem

14 cm

Choice.D

This is not correct because it does not match the calculated length for diagonal AC, which is 10 cm by using Pythagoras’s theorem

16 cm

Answer

Option

SumUp

Can you summarize what you’ve understood in the above steps?