Question

The base of a triangle is seven more than twice the height. The area of a triangle is 186 yd.² find the measure of the base in the height of the triangle

Answer 1

The height of Triangle is 12 yd and

The base of Triangle is 31 yd

Explanation:

Given as :

The area of triangle = 186 yd²

Let the height of triangle = h

So, base of triangle = 7 + 2 h

Now,

∵ The area of triangle =
`(1)/(2)* base* height`

Or, 186 yd² =
`(1)/(2)* (7+2h)* h`

Or, 186 × 2 = h × ( 7 +2h )

Or, 372 = 7 h + 2 h²

Or, 2 h² + 7 h - 372 = 0

So , 2 h² - 24 h + 31 h - 372 = 0

Or, 2 h ( h - 12 ) + 31 ( h - 12 ) = 0

Or, ( h - 12 ) ( 2 h + 31 ) = 0

SO, h - 12 = 0 And 2 h + 31 = 0

∴ h = 12 yd And h =
`(-31)/(2)`

SO, the Height of triangle = h = 12 yd and

The base of triangle = 2 × 12 + 7 = 24 + 7 = 31 yd

Base = 31 yd

Hence The height of Triangle is 12 yd and The base of Triangle is 31 yd Answer