Question

The base of a triangle is 3/4 of the length of the corresponding altitude. If the altitude is increased by 3 cm and the base is decreased by 2 cm, the area of the triangle remains the same. Find the base and altitude of the triangle

Answer 1

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 you understand

if you have any doubts feel free to comment ;)(

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 you understand