Question

The base of triangle is 3/4 the length of the corresponding altitude. if the altitude is increased by 3cm and the base is decreased by 2cm the area of the triangle remains the same. find the base and altitude of the triangle​

Answer 1

Answer:

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Answer 2

Answer:

let "l" be the length of altitude and "b" be the base

given base is equal to 3/4 of altitude in length

b = ( 3/4 ) l

area(A) = 1/2 * base * height

A = 1/2 * 3/4 l * l = (3/8) l²

if l is increased by 3, b decreases by 2

( l + 3 ) be the new altitude

( b - 2) be the new base

area ( A ' ) = 1/2 * ( l + 3 ) ( b - 2) = 1/2 *(l+3)*(3/4 l -2)

given A = A'

(3/8) l² = (1/8) * ( l + 3) * (3l - 8 )

3l² = 3l² + l -24

l = 24 ( altitude length)

b = (3/4) l = (3/4) *24 = 3*6 = 18 ( base length)

Hope this helps!