Squake ABCD, DC
(5a - 17 cm
and BC (2a +4)em, find the
length of
AD and
and AC.
Answers
Step-by-step explanation:
as all sides of a square are equal
DC = BC
5a - 17 = 2a + 4
5a - 2a = 17 + 4
3a. = 21
a = 7.....
DC = 5a - 17 = 5(7) - 17 = 35 - 17 = 18
BC = 2a + 4 = 2(7) + 4 = 14 + 4 = 18
AB = BC = CD = DA = 18cm....
Correct Question:
In square ABCD, DC = ( 5a - 17 ) cm and BC = ( 2a + 4 ) cm. Find the length of AD and AC.
Answer:
The length of AD is 18 cm.
The length of AC is 18 √2 cm.
Step-by-step-explanation:
NOTE: Refer to the attachment for the diagram.
In figure, □ ABCD is a square.
∴ AB = BC = CD = AD - - ( 1 ) [ Sides of a square ]
Now,
DC = BC - - [ From ( 1 ) ]
→ ( 5a - 17 ) = ( 2a + 4 ) - - [ Given ]
→ 5a - 17 = 2a + 4
→ 5a - 2a = 4 + 17
→ 3a = 21
→ a = 21 ÷ 3
→ a = 7
Now,
DC = ( 5a - 17 ) - - [ Given ]
→ DC = 5 × 7 - 17
→ DC = 35 - 17
∴ DC = 18 cm
Similarly,
AB = BC = AD = DC = 18 cm - - ( 2 ) [ From ( 1 ) ]
Now, in ΔADC, ∠ADC = 90° - - [ Angle of a square ]
∴ ( AC )² = ( AD )² + ( DC )² - - [ Pythagors theorem ]
→ AC² = ( 18 )² + ( 18 )² - - [ From ( 2 ) ]
→ AC² = 324 + 324
→ AC² = 648
→ AC = √(648) - - [ Taking square roots ]
→ AC = √( 324 × 2 )
→ AC = √( 18 × 18 × 2 )
→ AC = 18 √2 cm
Alternative Method:
From figure, we know that, AC is the diagonal of square.
To find the length of the diagonal of square, we can use the following formula:
Diagonal of square = side √2
→ AC = side √2
→ AC = AD √2
→ AC = 18 √2 cm - - [ From ( 2 ) ]
