Question

ɪᴛᴢ ᴜʀɢᴇɴᴛ...ᴅᴏɴᴛ sᴘᴀᴍ ɪ ᴡɪʟʟ ʀᴇᴘᴏʀᴛ ᴜʀ ᴀɴsᴡᴇʀs ᴀɴᴅ ǫᴜᴇsᴛɪᴏɴ..ɴᴏ ɴᴇᴇᴅ ᴛᴏ ᴡɪsʜ ᴍᴇ ᴄʜʀɪsᴛᴍᴀs ​

Answer 1

sides of triangle = 50,30,40

semi perimeter of the triangle = 50 + 30 + 40

2

= 120 = 60m

2

heron's formula = √s(s -a)(s -b)(s -c)

√60(60 -50)(60-30)(60-40)

√60×10×30×20

=600m

2× area of triangle = area of parallelogram

= 2×600 =12,000

area of parallelogram = base × height

50×height = 12,000

height = 12,000 = 240

50

hope it helps you

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Answer 2

Question :

A triangle and a Parallelogram stands on the same base of 50 m and have same area. If other sides of the triangle are 30 m and 40 m, find the corresponding base of the parallelogram.

Answer :

• Height of the parallelogram is 30 m.

Explanation :

Given :

• Base of the Parallelogram and the base of the triangle, b = 50 m.
• Sides of the triangle, b = 30 m and c = 40 m.

To find :

• Corresponding height of the parallelogram, h = ?

Knowledge required :

• Formula for semi-perimeter of a triangle, s = (a + b + c)/2

[Where : a,b and c are the sides of the triangle]

• Formula for area of a triangle, A = √[s(s - a)(s - b)(s - c)]

[Where : a,b and c are the sides of the triangle and s is the semi-perimeter of the triangle]

• Formula for area of a parallelogram, A = bh

[Where : b and h are the base and height of the parallelogram, respectively]

Solution :

To find the semi-perimeter of the triangle :

⠀⠀By using the formula for semi-perimeter of a triangle and substituting the values in it, we get :

⠀⠀=> s = (a + b + c)/2

⠀⠀=> s = (50 + 30 + 40)/2

⠀⠀=> s = 120/2

⠀⠀=> s = 60

⠀⠀⠀∴ s = 60 m

Hence the semi-perimeter of the triangle is 60 m.

To find the area of the triangle :

⠀⠀By using the formula for area of a triangle and substituting the values in it, we get :

⠀⠀=> A = √[s(s - a)(s - b)(s - c)]

⠀⠀=> A = √[60(60 - 50)(60 - 40)(60 - 30)]

⠀⠀=> A = √[60 × 10 × 20 × 30]

⠀⠀=> A = √[360000]

⠀⠀=> A = 600

⠀⠀⠀∴ A = 600 m²

Hence the area of the triangle is 600 m².

To find the height of the parallelogram :

⠀⠀By using the formula for area of a parallelogram and substituting the values in it, we get :

⠀⠀=> A = bh

⠀⠀=> 600 = 50 × h

⠀⠀=> 600/50 = h

⠀⠀=> 30 = h

⠀⠀⠀∴ h = 30 m

Therefore,

• The height of the parallelogram is 30 m.