Question

In a triangle ABC, the length of the
side BC is less than twice the length
of the side AB by 2 cm. The length of
the side AC is more than the length
of the side AB by 10 cm. If the
perimeter of the triangle is 40 cm,
what is the length of its shortest
side?
(1) 6 cm
(2) 7 cm
(3) 8 cm
(4) 10 cm​

Answer 1

Answer:

(3)8cm

Step-by-step explanation:

let AB be x

2x-2+x+10+x=40

4x+8=40

4x=32

x=8

other sides

2*8-2=16-2=14

8+10=18

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Answer 2

Answer:

Length of the shortest side of triangle is 8 cm.

Step-by-step explanation:

Given that :

• Side BC is less than twice the length
• of the side AB by 2 cm = 2AB - BC = 2 cm
• length of the side AC is more than the length of the side AB by 10 cm = AC - AB = 10 cm
• Perimeter of triangle = 40 cm

Solution :

• Let, 2AB - BC = 2 cm ---(1)
• AC - AB = 10 cm ---(2)
• AB + BC + AC = 40 ---(3)
• Adding equation (1) and (2), we get;
• AB + AC - BC = 12 ---(4)
• Adding equation (4) in equation (3), we get;
• 2(AB + AC) = 52 cm

⇒ AB + AC = 26 ---(5)

• putting value from equation (5) in equation (3), we get;
• BC +26 = 40

⇒ BC = 40 - 26 = 14 cm ---(6)

• putting value of BC in equation (1), we get;
• 2AB - 14 = 2

⇒ AB = 8 cm ---(7)

• Now, putting value from equation (6) and (7) in equation (3), we get;
• 8 + 14 + AC = 40

⇒ AC = 18 cm .

• Length of the shortest side of triangle is 8 cm.