Question

altitude of a triangle is 5 metre less than its base the area of the triangle is 42 square metre its base and altitude

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Answer 1

Answer:

The base and height are 6m and 11m respectively.

Step-by-step explanation:

Let the base be x

Therefore, Height = x-5

Given, Area = 42 m²

Area = 1/2 × b × h

42 = 1/2 × x × (x-5) => 42 = 1/2 × x²-5x

=> 42 = x²-5x/2 => x²-5x = 84 => x²-5x+16 = 100

=> x²-5x+4² = 100 => (x+4)² = 100 => x+4 = 10

=> x = 10 - 4 = 6

Base = x = 6 (answer).

Height = x+5 = 6+5 = 11 (answer).

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Answer 2

Given : altitude of a triangle is 5 metre less than its base.  the area of the triangle is 42 square metre

To find :  base and altitude

Solution:

Let say Base of Triangle =  B  m

Altitude of a triangle is 5 metre less than its base

=> Altitude  = B - 5  m

area of the triangle  = (1/2) * Base * Altitude

=> 42 = (1/2) B(B - 5)

=> 84 = B² - 5B

=> B² - 5B - 84 = 0

=> B² - 12B + 7B - 84 = 0

=> B(B - 12) + 7(B - 12) = 0

=> ( B + 7)(B - 12) = 0

=> B = 12     as B = -7 not possible ∵ base can not be -ve

∴ Base = 12 m

Altitude = 12 - 5 = 7 m

Base = 12 m & Altitude = 7 m

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