Question

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

please solve the question but if you don't Know no need to answer​

Answer 1

Answer:

answer: h = -4 units

b= -1.6 units

Answer 2

Answer:

Altitude = 20 cm

Base = 8 cm

Step-by-step explanation:

Given:

• Base of the triangle = 2/5 the length of the altitude
• If the altitude is decreased by 4 cm and the base is increased by 2cm, the area of the triangle remains the same

To Find:

• The base and altitude of the triangle

Solution:

By given,

Base of the triangle = 2/5 × altitude

b = 2/5 × h------(1)

The area of a triangle is given by,

Area of a triangle = 1/2 × b × h

Substitute the value of b from equation 1

Area of traingle = 1/2 × 2/5 × h × h

Area of triangle = h²/5 ------(2)

Now if the altitude is decreased by 4 cm and base increased by 2 cm, the new altitude and base is given by,

New altitude = h - 4

New base = 2/5 h + 2

New base = (2h + 10)/5

Area of the triangle  = 1/2 × (2h + 10)/5 × (h - 4)

Area of the triangle = 1/2 × 2 (h + 5)/5 × (h - 4)

Area of the triangle = (h + 5)/5 × (h - 4) ------(3)

By given the LHS of equation 2 and 3 are equal. Hence RHS must also be equal.

h²/5 = (h + 5)/5 × (h - 4)

Cancelling 5 on both sides,

h² = (h + 5) (h - 4)

h² = h² -4h + 5h -20

h - 20 = 0

h = 20

Hence altitude of the triangle is 20 cm.

Now substitute the value of h in equation 1

b = 2/5 × 20

b = 2 × 4

b = 8 cm

Hence base of the triangle is 8 cm.