Question

The base of a triangle is twice its height. if the area is 49 find the base and the height

Answer 1

The height of triangle is 7 units and base of triangle is 14 units

Solution:

The area of triangle is given by formula:

`\text{Area of triangle } = (1)/(2) * b * h`

Where,

"b" is the base and "h" is the height of triangle

Given in question that,

Area = 49 square units

Also given that, base of a triangle is twice its height

Base of triangle = twice the height

b = 2h

Substituting the values in formula,

`49 = (1)/(2) * 2h * h\\\\49 = h^2\\\\\text{Taking square root on both sides }\\\\h = \pm 7`

Since, height cannot be negative, ignore -7

The solution is h = 7

Substitute h = 7 in b = 2h

b = 2h

b = 2(7)

b = 14

Thus height of triangle is 7 units and base of triangle is 14 units